(22015^7758 


THE  UNIVERSITY  LIBRARY 

6F  SAUFORNIA,  SAN  DIEGO 
JOLLA,  CALIFORNIA 


H.  J.  MACEVOY 


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University  of  California,  San  Diego 
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UNIVERSITY  OF  CALIFORNIA,  SAN  DIEGO 


3  1822015824758 


MYSTICISM    AND    LOGIC 
AND  OTHER   ESSAYS 


MYSTICISM   AND 
LOGIC 

AND  OTHER  ESSAYS 


BY 

BERTRAND   RUSSELL,    M.A.,    F.R.S. 


LONGMANS,   GREEN   AND  CO, 

39    PATERNOSTER    ROW,    LONDON 

FOURTH  AVENUE  &  3OTH  STREET,  NEW  YORK 

BOMBAY,     CALCUTTA     AND     MADRAS 

1918 

All  rights  reserved 


PREFACE 

r  I  ^HE  following  essays  have  been  written  and  pub- 
•1  lished  at  various  times,  and  my  thanks  are  due  to 
the  previous  publishers  for  the  permission  to  reprint 
them. 

The  essay  on  "  Mysticism  and  Logic  "  appeared  in  the 
Hibbert  Journal  for  July,  1914.  "  The  Place  of  Science 
in  a  Liberal  Education  "  appeared  in  two  numbers  of 
The  New  Statesman,  May  24  and  31,  1913.  "  The  Free 
Man's  Worship  "  and  "  The  Study  of  Mathematics  " 
were  included  in  a  former  collection  (now  out  of  print), 
Philosophical  Essays,  also  published  by  Messrs.  Longmans, 
Green  &  Co.  Both  were  written  in  1902 ;  the  first  appeared 
originally  in  the  Independent  Review  for  1903,  the  second 
in  the  New  Quarterly,  November,  1907.  In  theoretical 
Ethics,  the  position  advocated  in  "  The  Free  Man's 
Worship "  is  not  quite  identical  with  that  which  I 
hold  now  :  I  feel  less  convinced  than  I  did  then  of  the 
objectivity  of  good  and  evil.  But  the  general  attitude 
towards  life  which  is  suggested  in  that  essay  still  seems 
to  me,  in  the  main,  the  one  which  must  be  adopted  in 
times  of  stress  and  difficulty  by  those  who  have  no 
dogmatic  religious  beliefs,  if  inward  defeat  is  to  be 
avoided. 

The  essay  on  "  Mathematics  and  the  Metaphysicians  " 
was  written  in  1901,  and  appeared  in  an  American  maga- 
zine, The  International  Monthly,  under  the  title  "  Recent 
Work  in  the  Philosophy  of  Mathematics."  Some  points 


vi  MYSTICISM   AND   LOGIC 

in  this  essay  require  modification  in  view  of  later  work. 
These  are  indicated  in  footnotes.  Its  tone  is  partly 
explained  by  the  fact  that  the  editor  begged  me  to  make 
the  article  "  as  romantic  as  possible." 

All  the  above  essays  are  entirely  popular,  but  those 
that  follow  are  somewhat  more  technical.  "  On  Scientific 
Method  in  Philosophy  "  was  the  Herbert  Spencer  lecture 
at  Oxford  in  1914,  and  was  published  by  the  Clarendon 
Press,  which  has  kindly  allowed  me  to  include  it  in  this 
collection.  "The  Ultimate  Constituents  of  Matter" 
was  an  address  to  the  Manchester  Philosophical  Society, 
early  in  1915,  and  was  published  in  the  Monist  in  July 
of  that  year.  The  essay  on  "  The  Relation  of  Sense-data 
to  Physics  "  was  written  in  January,  1914,  and  first 
appeared  in  No.  4  of  that  year's  volume  of  Scientia,  an 
International  Review  of  Scientific  Synthesis,  edited  by 
M.  Eugenio  Rignano,  published  monthly  by  Messrs. 
Williams  and  Norgate,  London,  Nicola  Zanichelli, 
Bologna,  and  Felix  Alcan,  Paris.  The  essay  "On  the 
Notion  of  Cause  "  was  the  presidential  address  to  the 
Aristotelian  Society  in  November,  1912,  and  was  pub- 
lished in  their  Proceedings  for  1912-13.  "  Knowledge  by 
Acquaintance  and  Knowledge  by  Description  "  was  also 
a  paper  read  before  the  Aristotelian  Society,  and  pub- 
lished in  their  Proceedings  for  1910-11. 

LONDON, 

September,  1917. 


CONTENTS 

CHAP.  PAGE 

I.  MYSTICISM  AND  LOGIC               .  i 

II.  THE  PLACE  OF  SCIENCE  IN  A  LIBERAL  EDUCATION  33 

III.  A  FREE  MAN'S  WORSHIP           .              .  46 

IV.  THE  STUDY  OF  MATHEMATICS   .              .  58 
V.  MATHEMATICS  AND  THE  METAPHYSICIANS         .       .  74 

VI.  ON  SCIENTIFIC  METHOD  IN  PHILOSOPHY           .       .  97 

VII.  THE  ULTIMATE  CONSTITUENTS  OF  MATTER       .       .125 

VIII.  THE  RELATION  OF  SENSE-DATA  TO  PHYSICS      .       .  145 

IX.  ON  THE  NOTION  OF  CAUSE        .              .           .       .  180 

X.  KNOWLEDGE  BY  ACQUAINTANCE  AND  KNOWLEDGE  BY 

DESCRIPTION             .              .              ...  209 


VII 


MYSTICISM  AND   LOGIC 
AND  OTHER  ESSAYS 


MYSTICISM   AND   LOGIC 

METAPHYSICS,  or  the  attempt  to  conceive  the 
world  as  a  whole  by  means  of  thought,  has  been 
developed,  from  the  first,  by  the  union  and  conflict  of 
two  very  different  human  impulses,  the  one  urging  men 
towards  mysticism,  the  other  urging  them  towards 
science.  Some  men  have  achieved  greatness  through 
one  of  these  impulses  alone,  others  through  the  other 
alone  :  in  Hume,  for  example,  the  scientific  impulse 
reigns  quite  unchecked,  while  in  Blake  a  strong  hostility 
to  science  co-exists  with  profound  mystic  insight.  But 
the  greatest  men  who  have  been  philosophers  have  felt 
the  need  both  of  science  and  of  mysticism  :  the  attempt 
to  harmonise  the  two  was  what  made  their  life,  and  what 
always  must,  for  all  its  arduous  uncertainty,  make 
philosophy,  to  some  minds,  a  greater  thing  than  either 
science  or  religion. 

Before  attempting  an  explicit  characterisation  of  the 
scientific  and  the  mystical  impulses,  I  will  illustrate 
them  by  examples  from  two  philosophers  whose  great- 
ness lies  in  the  very  intimate  blending  which  they 
achieved.  The  two  philosophers  I  mean  are  Heraclitus 
and  Plato. 


2  MYSTICISM    AND   LOGIC 

Heraclitus,  as  every  one  knows,  was  a  believer  in 
universal  flux :  time  builds  and  destroys  all  things. 
From  the  few  fragments  that  remain,  it  is  not  easy  to 
discover  how  he  arrived  at  his  opinions,  but  there  are 
some  sayings  that  strongly  suggest  scientific  observation 
as  the  source. 

"  The  things  that  can  be  seen,  heard,  and  learned,"  he 
says,  "  are  what  I  prize  the  most."  This  is  the  language 
of  the  empiricist,  to  whom  observation  is  the  sole  guaran- 
tee of  truth.  "  The  sun  is  new  every  day,"  is  another 
fragment ;  and  this  opinion,  in  spite  of  its  paradoxical 
character,  is  obviously  inspired  by  scientific  reflection, 
and  no  doubt  seemed  to  him  to  obviate  the  difficulty  of 
understanding  how  the  sun  can  work  its  way  under- 
ground from  west  to  east  during  the  night.  Actual 
observation  must  also  have  suggested  to  him  his  central 
doctrine,  that  Fire  is  the  one  permanent  substance,  of 
which  all  visible  things  are  passing  phases.  In  com- 
bustion we  see  things  change  utterly,  while  their  flame 
and  heat  rise  up  into  the  air  and  vanish. 

"  This  world,  which  is  the  same  for  all,"  he  says,  "  no 
one  of  gods  or  men  has  made  ;  but  it  was  ever,  is  now, 
and  ever  shall  be,  an  ever-living  Fire,  with  measures 
kindling,  and  measures  going  out." 

"  The  transformations  of  Fire  are,  first  of  all,  sea  ;  and 
half  of  the  sea  is  earth,  half  whirlwind." 

This  theory,  though  no  longer  one  which  science  can 
accept,  is  nevertheless  scientific  in  spirit.  Science,  too, 
might  have  inspired  the  famous  saying  to  which  Plato 
alludes  :  "  You  cannot  step  twice  into  the  same  rivers  ; 
for  fresh  waters  are  ever  flowing  in  upon  you."  But  we 
find  also  another  statement  among  the  extant  fragments  : 
"  We  step  and  do  not  step  into  the  same  rivers  ;  we  are 
and  are  not." 


MYSTICISM   AND   LOGIC  3 

The  comparison  of  this  statement,  which  is  mystical, 
with  the  one  quoted  by  Plato,  which  is  scientific,  shows 
how  intimately  the  two  tendencies  are  blended  in  the 
system  of  Heraclitus.  Mysticism  is,  in  essence,  little 
more  than  a  certain  intensity  and  depth  of  feeling  in 
regard  to  what  is  believed  about  the  universe  ;  and  this 
kind  of  feeling  leads  Heraclitus,  on  the  basis  of  his  science, 
to  strangely  poignant  sayings  concerning  life  and  the 
world,  such  as  : 

"  Time  is  a  child  playing  draughts,  the  kingly  power  is 
a  child's." 

It  is  poetic  imagination,  not  science,  which  presents 
Time  as  despotic  lord  of  the  world,  with  all  the  irrespon- 
sible frivolity  of  a  child.  It  is  mysticism,  too,  which 
leads  Heraclitus  to  assert  the  identity  of  opposites  : 
"  Good  and  ill  are  one,"  he  says  ;  and  again  :  "  To  God 
all  things  are  fair  and  good  and  right,  but  men  hold  some 
things  wrong  and  some  right." 

Much  of  mysticism  underlies  the  ethics  of  Heraclitus. 
It  is  true  that  a  scientific  determinism  alone  might  have 
inspired  the  statement :  "  Man's  character  is  his  fate  "  ; 
but  only  a  mystic  would  have  said  : 

"  Every  beast  is  driven  to  the  pasture  with  blows  "  ; 
and  again  : 

"It  is  hard  to  fight  with  one's  heart's  desire.  What- 
ever it  wishes  to  get,  it  purchases  at  the  cost  of  soul "  ; 
and  again  : 

"  Wisdom  is  one  thing.  It  is  to  know  the  thought  by 
which  all  things  are  steered  through  all  things."1 

Examples  might  be  multiplied,  but  those  that  have 
been  given  are  enough  to  show  the  character  of  the  man  : 
the  facts  of  science,  as  they  appeared  to  him,  fed  the 

1  All  the  above  quotations  are  from  Burnet's  Early  Greek  Philo- 
sophy, (and  ed.,  1908),  pp.  146-156. 


4  MYSTICISM   AND   LOGIC 

flame  in  his  soul,  and  in  its  light  he  saw  into  the  depths 
of  the  world  by  the  reflection  of  his  own  dancing  swiftly 
penetrating  fire.  In  such  a  nature  we  see  the  true  union 
of  the  mystic  and  the  man  of  science — the  highest 
eminence,  as  I  think,  that  it  is  possible  to  achieve  in  the 
world  of  thought. 

In  Plato,  the  same  twofold  impulse  exists,  though  the 
mystic  impulse  is  distinctly  the  stronger  of  the  two,  and 
secures  ultimate  victory  whenever  the  conflict  is  sharp. 
His  description  of  the  cave  is  the  classical  statement  of 
belief  in  a  knowledge  and  reality  truer  and  more  real 
than  that  of  the  senses  : 

"  Imagine  1  a  number  of  men  living  in  an  underground 
cavernous  chamber,  with  an  entrance  open  to  the  light, 
extending  along  the  entire  length  of  the  cavern,  in  which 
they  have  been  confined,  from  their  childhood,  with  their 
legs  and  necks  so  shackled  that  they  are  obliged  to  sit 
still  and  look  straight  forwards,  because  their  chains 
render  it  impossible  for  them  to  turn  their  heads  round  : 
and  imagine  a  bright  fire  burning  some  way  off,  above 
and  behind  them,  and  an  elevated  roadway  passing 
between  the  fire  and  the  prisoners,  with  a  low  wall  built 
along  it,  like  the  screens  which  conjurors  put  up  in  front 
of  their  audience,  and  above  which  they  exhibit  their 
wonders. 

I  have  it,  he  replied. 

Also  figure  to  yourself  a  number  of  persons  walking 
behind  this  wall,  and  carrying  with  them  statues  of  men, 
and  images  of  other  animals,  wrought  in  wood  and  stone 
and  all  kinds  of  materials,  together  with  various  other 
articles,  which  overtop  the  wall ;  and,  as  you  might 
expect,  let  some  of  the  passers-by  be  talking,  and  others 
silent. 

1  Republic,  514,  translated  by  Davies  and  Vaughan. 


MYSTICISM    AND   LOGIC  5 

You  are  describing  a  strange  scene,  and  strange 
prisoners. 

They  resemble  us,  I  replied. 

Now  consider  what  would  happen  if  the  course  of 
nature  brought  them  a  release  from  their  fetters,  and  a 
remedy  for  their  foolishness,  in  the  following  manner. 
Let  us  suppose  that  one  of  them  has  been  released,  and 
compelled  suddenly  to  stand  up,  and  turn  his  neck  round 
and  walk  with  open  eyes  towards  the  light ;  and  let  us 
suppose  that  he  goes  through  all  these  actions  with  pain, 
and  that  the  dazzling  splendour  renders  him  incapable  of 
discerning  those  objects  of  which  he  used  formerly  to  see 
the  shadows.  What  answer  should  you  expect  him  to 
make,  if  some  one  were  to  tell  him  that  in  those  days  he 
was  watching  foolish  phantoms,  but  that  now  he  is  some- 
what nearer  to  reality,  and  is  turned  towards  things  more 
real,  and  sees  more  correctly ;  above  all,  if  he  were  to 
point  out  to  him  the  several  objects  that  are  passing  by, 
and  question  him,  and  compel  him  to  answer  what  they 
are  ?  Should  you  not  expect  him  to  be  puzzled,  and  to 
regard  his  old  visions  as  truer  than  the  objects  now  forced 
upon  his  notice  ? 

Yes,  much  truer.  .  .  . 

Hence,  I  suppose,  habit  will  be  necessary  to  enable  him 
to  perceive  objects  in  that  upper  world.  At  first  he  will 
be  most  successful  in  distinguishing  shadows  ;  then  he 
will  discern  the  reflections  of  men  and  other  things  in 
water,  and  afterwards  the  realities  ;  and  after  this  he  will 
raise  his  eyes  to  encounter  the  light  of  the  moon  and  stars, 
finding  it  less  difficult  to  study  the  heavenly  bodies  and 
the  heaven  itself  by  night,  than  the  sun  and  the  sun's  light 
by  day. 

Doubtless. 

Last  of  all,  I  imagine,  he  will  be  able  to  observe  and 


6  MYSTICISM   AND   LOGIC 

contemplate  the  nature  of  the  sun,  not  as  it  appears  in 
water  or  on  alien  ground,  but  as  it  is  in  itself  in  its  own 
territory. 

Of  course. 

His  next  step  will  be  to  draw  the  conclusion,  that  the 
sun  is  the  author  of  the  seasons  and  the  years,  and  the 
guardian  of  all  things  in  the  visible  world,  and  in  a  manner 
the  cause  of  all  those  things  which  he  and  his  companions 
used  to  see. 

Obviously,  this  will  be  his  next  step.  .  .  . 

Now  this  imaginary  case,  my  dear  Glancon,  you  must 
apply  in  all  its  parts  to  our  former  statements,  by  com- 
paring the  region  which  the  eye  reveals,  to  the  prison 
house,  and  the  light  of  the  fire  therein  to  the  power  of  the 
sun  :  and  if,  by  the  upward  ascent  and  the  contemplation 
of  the  upper  world,  you  understand  the  mounting  of  the 
soul  into  the  intellectual  region,  you  will  hit  the  tendency 
of  my  own  surmises,  since  you  desire  to  be  told  what  they 
are  ;  though,  indeed,  God  only  knows  whether  they  are 
correct.  But,  be  that  as  it  may,  the  view  which  I  take  of 
the  subject  is  to  the  following  effect.  In  the  world  of 
knowledge,  the  essential  Form  of  Good  is  the  limit  of  our 
enquiries,  and  can  barely  be  perceived ;  but,  when 
perceived,  we  cannot  help  concluding  that  it  is  in  every 
case  the  source  of  all  that  is  bright  and  beautiful, — in  the 
visible  world  giving  birth  to  light  and  its  master,  and  in 
the  intellectual  world  dispensing,  immediately  and  with 
full  authority,  truth  and  reason  ; — and  that  whosoever 
would  act  wisely,  either  in  private  or  in  public,  must  set 
this  Form  of  Good  before  his  eyes." 

But  in  this  passage,  as  throughout  most  of  Plato's 
teaching,  there  is  an  identification  of  the  good  with  the 
truly  real,  which  became  embodied  in  the  philosophical 


MYSTICISM   AND   LOGIC  7 

tradition,  and  is  still  largely  operative  in  our  own  day. 
In  thus  allowing  a  legislative  function  to  the  good,  Plato 
produced  a  divorce  between  philosophy  and  science, 
from  which,  in  my  opinion,  both  have  suffered  ever  since 
and  are  still  suffering.  The  man  of  science,  whatever  his 
hopes  may  be,  must  lay  them  aside  while  he  studies 
nature ;  and  the  philosopher,  if  he  is  to  achieve  truth 
must  do  the  same.  Ethical  considerations  can  only 
legitimately  appear  when  the  truth  has  been  ascertained  : 
they  can  and  should  appear  as  determining  our  feeling 
towards  the  truth,  and  our  manner  of  ordering  our  lives 
in  view  of  the  truth,  but  not  as  themselves  dictating  what 
the  truth  is  to  be. 

There  are  passages  in  Plato — among  those  which  illus- 
trate the  scientific  side  of  his  mind — where  he  seems 
clearly  aware  of  this.  The  most  noteworthy  is  the  one 
in  which  Socrates,  as  a  young  man,  is  explaining  the 
theory  of  ideas  to  Parmenides. 

After  Socrates  has  explained  that  there  is  an  idea  of 
the  good,  but  not  of  such  things  as  hair  and  mud  and 
dirt,  Parmenides  advises  him  "  not  to  despise  even  the 
meanest  things,"  and  this  advice  shows  the  genuine 
scientific  temper.  It  is  with  this  impartial  temper  that 
the  mystic's  apparent  insight  into  a  higher  reality  and  a 
hidden  good  has  to  be  combined  if  philosophy  is  to  realise 
its  greatest  possibilities.  And  it  is  failure  in  this  respect 
that  has  made  so  much  of  idealistic  philosophy  thin, 
lifeless,  and  insubstantial.  It  is  only  in  marriage  with 
the  world  that  our  ideals  can  bear  fruit  :  divorced  from 
it,  they  remain  barren.  But  marriage  with  the  world  is 
not  to  be  achieved  by  an  ideal  which  shrinks  from  fact, 
or  demands  in  advance  that  the  world  shall  conform  to 
its  desires. 

Parmenides   himself   is   the   source   of   a    peculiarly 


8  MYSTICISM   AND   LOGIC 

interesting  strain  of  mysticism  which  pervades  Plato's 
thought — the  mysticism  which  may  be  called  "  logical  " 
because  it  is  embodied  in  theories  on  logic.  This  form  of 
mysticism,  which  appears,  so  far  as  the  West  is  con- 
cerned, to  have  originated  with  Parmenides,  dominates 
the  reasonings  of  all  the  great  mystical  metaphysicians 
from  his  day  to  that  of  Hegel  and  his  modern  disciples. 
Reality,  he  says,  is  uncreated,  indestructible,  unchanging, 
indivisible  ;  it  is  "  immovable  in  the  bonds  of  mighty 
chains,  without  beginning  and  without  end  ;  since  coming 
into  being  and  passing  away  have  been  driven  afar,  and 
true  belief  has  cast  them  away."  The  fundamental 
principle  of  his  inquiry  is  stated  in  a  sentence  which 
would  not  be  out  of  place  in  Hegel :  "  Thou  canst  not 
know  what  is  not — that  is  impossible — nor  utter  it ;  for 
it  is  the  same  thing  that  can  be  thought  and  that  can  be." 
And  again  :  "  It  needs  must  be  that  what  can  be  thought 
and  spoken  of  is  ;  for  it  is  possible  for  it  to  be,  and  it  is 
not  possible  for  what  is  nothing  to  be."  The  impossi- 
bility of  change  follows  from  this  principle  ;  for  what  is 
past  can  be  spoken  of,  and  therefore,  by  the  principle, 
still  is. 

Mystical  philosophy,  in  all  ages  and  in  all  parts  of  the 
world,  is  characterised  by  certain  beliefs  which  are  illus- 
trated by  the  doctrines  we  have  been  considering. 

There  is,  first,  the  belief  in  insight  as  against  discur- 
sive analytic  knowledge  :  the  belief  in  a  way  of  wisdom, 
sudden,  penetrating,  coercive,  which  is  contrasted  with 
the  slow  and  fallible  study  of  outward  appearance  by  a 
science  relying  wholly  upon  the  senses.  All  who  are 
capable  of  absorption  in  an  inward  passion  must  have 
experienced  at  times  the  strange  feeling  of  unreality  in 
common  objects,  the  loss  of  contact  with  daily  things,  in 
which  the  solidity  of  the  outer  world  is  lost,  and  the  soul 


MYSTICISM   AND   LOGIC  9 

seems,  in  utter  loneliness,  to  bring  forth,  out  of  its  own 
depths,  the  mad  dance  of  fantastic  phantoms  which  have 
hitherto  appeared  as  independently  real  and  living. 
This  is  the  negative  side  of  the  mystic's  initiation  :  the 
doubt  concerning  common  knowledge,  preparing  the  way 
for  the  reception  of  what  seems  a  higher  wisdom.  Many 
men  to  whom  this  negative  experience  is  familiar  do  not 
pass  beyond  it,  but  for  the  mystic  it  is  merely  the  gateway 
to  an  ampler  world. 

The  mystic  insight  begins  with  the  sense  of  a  mystery 
unveiled,  of  a  hidden  wisdom  now  suddenly  become 
certain  beyond  the  possibility  of  a  doubt.  The  sense  of 
certainty  and  revelation  comes  earlier  than  any  definite 
belief.  The  definite  beliefs  at  which  mystics  arrive  are 
the  result  of  reflection  upon  the  inarticulate  experience 
gained  in  the  moment  of  insight.  Often,  beliefs  which 
have  no  real  connection  with  this  moment  become  subse- 
quently attracted  into  the  central  nucleus  ;  thus  in  addi- 
tion to  the  convictions  which  all  mystics  share,  we  find, 
in  many  of  them,  other  convictions  of  a  more  local  and 
temporary  character,  which  no  doubt  become  amalga- 
mated with  what  was  essentially  mystical  in  virtue  of 
their  subjective  certainty.  We  may  ignore  such  inessential 
accretions,  and  confine  ourselves  to  the  beliefs  which  all 
mystics  share. 

The  first  and  most  direct  outcome  of  the  moment  of 
illumination  is  belief  in  the  possibility  of  a  way  of  know- 
ledge which  may  be  called  revelation  or  insight  or  in- 
tuition, as  contrasted  with  sense,  reason,  and  analysis, 
which  are  regarded  as  blind  guides  leading  to  the  morass 
of  illusion.  Closely  connected  with  this  belief  is  the 
conception  of  a  Reality  behind  the  world  of  appearance 
and  utterly  different  from  it.  This  Reality  is  regarded 
with  an  admiration  often  amounting  to  worship ;  it  is 


io  MYSTICISM   AND   LOGIC 

felt  to  be  always  and  everywhere  close  at  hand,  thinly 
veiled  by  the  shows  of  sense,  ready,  for  the  receptive 
mind,  to  shine  in  its  glory  even  through  the  apparent 
folly  and  wickedness  of  Man.  The  poet,  the  artist,  and 
the  lover  are  seekers  after  that  glory  :  the  haunting 
beauty  that  they  pursue  is  the  faint  reflection  of  its  sun. 
But  the  mystic  lives  in  the  full  light  of  the  vision  :  what 
others  dimly  seek  he  knows,  with  a  knowledge  beside 
which  all  other  knowledge  is  ignorance. 

The  second  characteristic  of  mysticism  is  its  belief  in 
unity,  and  its  refusal  to  admit  opposition  or  division 
anywhere.  We  found  Heraclitus  saying  "  good  and  ill 
are  one  "  ;  and  again  he  says,  "  the  way  up  and  the  way 
down  is  one  and  the  same."  The  same  attitude  appears 
in  the  simultaneous  assertion  of  contradictory  pro- 
positions, such  as  :  "  We  step  and  do  not  step  into  the 
same  rivers  ;  we  are  and  are  not."  The  assertion  of  Par- 
menides,  that  reality  is  one  and  indivisible,  comes  from 
the  same  impulse  towards  unity.  In  Plato,  this  impulse 
is  less  prominent,  being  held  in  check  by  his  theory  of 
ideas  ;  but  it  reappears,  so  far  as  his  logic  permits,  in  the 
doctrine  of  the  primacy  of  the  Good. 

A  third  mark  of  almost  all  mystical  metaphysics  is  the 
denial  of  the  reality  of  Time.  This  is  an  outcome  of  the 
denial  of  division  ;  if  all  is  one,  the  distinction  of  past 
and  future  must  be  illusory.  We  have  seen  this  doctrine 
prominent  in  Parmenides ;  and  among  moderns  it  is 
fundamental  in  the  systems  of  Spinoza  and  Hegel. 

The  last  of  the  doctrines  of  mysticism  which  we  have 
to  consider  is  its  belief  that  all  evil  is  mere  appearance, 
an  illusion  produced  by  the  divisions  and  oppositions  of 
the  analytic  intellect.  Mysticism  does  not  maintain  that 
such  things  as  cruelty,  for  example,  are  good,  but  it 
denies  that  they  are  real :  they  belong  to  that  lower 


MYSTICISM   AND   LOGIC  11 

world  of  phantoms  from  which  we  are  to  be  liberated  by 
the  insight  of  the  vision.  Sometimes — for  example  in 
Hegel,  and  at  least  verbally  in  Spinoza — not  only  evil, 
but  good  also,  is  regarded  as  illusory,  though  nevertheless 
the  emotional  attitude  towards  what  is  held  to  be  Reality 
is  such  as  would  naturally  be  associated  with  the  belief 
that  Reality  is  good.  What  is,  in  all  cases,  ethically 
characteristic  of  mysticism  is  absence  of  indignation  or 
protest,  acceptance  with  joy,  disbelief  in  the  ultimate 
truth  of  the  division  into  two  hostile  camps,  the  good  and 
the  bad.  This  attitude  is  a  direct  outcome  of  the  nature 
of  the  mystical  experience  :  with  its  sense  of  unity  is 
associated  a  feeling  of  infinite  peace.  Indeed  it  may  be 
suspected  that  the  feeling  of  peace  produces,  as  feelings 
do  in  dreams,  the  whole  system  of  associated  beliefs 
which  make  up  the  body  of  mystic  doctrine.  But  this  is 
a  difficult  question,  and  one  on  which  it  cannot  be  hoped 
that  mankind  will  reach  agreement. 

Four  questions  thus  arise  in  considering  the  truth  or 
falsehood  of  mysticism,  namely  : 

I.  Are  there  two  ways  of  knowing,  which  may  be  called 
respectively  reason  and  intuition  ?    And  if  so,  is  either  to 
be  preferred  to  the  other  ? 

II.  Is  all  plurality  and  division  illusory  ? 

III.  Is  time  unreal  ? 

IV.  What  kind  of  reality  belongs  to  good  and  evil  ? 

On  all  four  of  these  questions,  while  fully  developed 
mysticism  seems  to  me  mistaken,  I  yet  believe  that,  by 
sufficient  restraint,  there  is  an  element  of  wisdom  to  be 
learned  from  the  mystical  way  of  feeling,  which  does  not 
seem  to  be  attainable  in  any  other  manner.  If  this  is  the 
truth,  mysticism  is  to  be  commended  as  an  attitude 
towards  life,  not  as  a  creed  about  the  world.  The  meta- 


12  MYSTICISM   AND   LOGIC 

physical  creed,  I  shall  maintain,  is  a  mistaken  outcome 
of  the  emotion,  although  this  emotion,  as  colouring  and 
informing  all  other  thoughts  and  feelings,  is  the  inspirer 
of  whatever  is  best  in  Man.  Even  the  cautious  and 
patient  investigation  of  truth  by  science,  which  seems 
the  very  antithesis  of  the  mystic's  swift  certainty,  may 
be  fostered  and  nourished  by  that  very  spirit  of  reverence 
in  which  mysticism  lives  and  moves. 


I.    REASON   AND   INTUITION1 

Of  the  reality  or  unreality  of  the  mystic's  world  I  know 
nothing.  I  have  no  wish  to  deny  it,  nor  even  to  declare 
that  the  insight  which  reveals  it  is  not  a  genuine  insight. 
What  I  do  wish  to  maintain — and  it  is  here  that  the 
scientific  attitude  becomes  imperative — is  that  insight, 
untested  and  unsupported,  is  an  insufficient  guarantee  of 
truth,  in  spite  of  the  fact  that  much  of  the  most  important 
truth  is  first  suggested  by  its  means.  It  is  common -to 
speak  of  an  opposition  between  instinct  and  reason  ;  in 
the  eighteenth  century,  the  opposition  was  drawn  in 
favour  of  reason,  but  under  the  influence  of  Rousseau  and 
the  romantic  movement  instinct  was  given  the  preference, 
first  by  those  who  rebelled  against  artificial  forms  of 
government  and  thought,  and  then,  as  the  purely 
rationalistic  defence  of  traditional  theology  became 
increasingly  difficult,  by  all  who  felt  in  science  a  menace 
to  creeds  which  they  associated  with  a  spiritual  outlook 
on  life  and  the  world.  Bergson,  under  the  name  of 
"intuition,"  has  raised  instinct  to  the  position  of  sole 

1  This  section,  and  also  one  or  two  pages  in  later  sections,  have  been 
printed  in  a  course  of  Lowell  lectures  On  our  knowledge  of  the  external 
world,  published  by  the  Open  Court  Publishing  Company.  But  I  have 
left  them  here,  as  this  is  the  context  for  which  they  were  originally 
written. 


MYSTICISM   AND   LOGIC  13 

arbiter  of  metaphysical  truth.  But  in  fact  the  opposi- 
tion of  instinct  and  reason  is  mainly  illusory.  Instinct, 
intuition,  or  insight  is  what  first  leads  to  the  beliefs 
which  subsequent  reason  confirms  or  confutes ;  but  the 
confirmation,  where  it  is  possible,  consists,  in  the  last 
analysis,  of  agreement  with  other  beliefs  no  less  in- 
stinctive. Reason  is  a  harmonising,  controlling  force 
rather  than  a  creative  one.  Even  in  the  most  purely 
logical  realm,  it  is  insight  that  first  arrives  at  what  is 
new. 

Where  instinct  and  reason  do  sometimes  conflict  is  in 
regard  to  single  beliefs,  held  instinctively,  and  held  with 
such  determination  that  no  degree  of  inconsistency  with 
other  beliefs  leads  to  their  abandonment.  Instinct,  like 
all  human  faculties,  is  liable  to  error.  Those  in  whom 
reason  is  weak  are  often  unwilling  to  admit  this  as 
regards  themselves,  though  all  admit  it  in  regard  to 
others.  Where  instinct  is  least  liable  to  error  is  in 
practical  matters  as  to  which  right  judgment  is  a  help  to 
survival :  friendship  and  hostility  in  others,  for  instance, 
are  often  felt  with  extraordinary  discrimination  through 
very  careful  disguises.  But  even  in  such  matters  a  wrong 
impression  may  be  given  by  reserve  or  flattery ;  and  in 
matters  less  directly  practical,  such  as  philosophy  deals 
with,  very  strong  instinctive  beliefs  are  sometimes  wholly 
mistaken,  as  we  may  come  to  know  through  their  per- 
ceived inconsistency  with  other  equally  strong  beliefs. 
It  is  such  considerations  that  necessitate  the  harmonising 
mediation  of  reason,  which  tests  our  beliefs  by  their 
mutual  compatibility,  and  examines,  in  doubtful  cases, 
the  possible  sources  of  error  on  the  one  side  and  on  the 
other.  In  this  there  is  no  opposition  to  instinct  as  a 
whole,  but  only  to  blind  reliance  upon  some  one  interest- 
ing aspect  of  instinct  to  the  exclusion  of  other  more 


14  MYSTICISM   AND   LOGIC 

commonplace  but  not  less  trustworthy  aspects.  It  is 
such  one-sidedness,  not  instinct  itself,  that  reason  aims 
at  correcting. 

These  more  or  less  trite  maxims  may  be  illustrated  by 
application  to  Bergson's  advocacy  of  "  intuition  "  as 
against  "  intellect."  There  are,  he  says,  "  two  profoundly 
different  ways  of  knowing  a  thing.  The  first  implies  that 
we  move  round  the  object :  the  second  that  we  enter 
into  it.  The  first  depends  on  the  point  of  view  at  which 
we  are  placed  and  on  the  symbols  by  which  we  express 
ourselves.  The  second  neither  depends  on  a  point  of 
view  nor  relies  on  any  symbol.  The  first  kind  of  knowledge 
may  be  said  to  stop  at  the  relative  ;  the  second,  in  those 
cases  where  it  is  possible,  to  attain  the  absolute."1  The 
second  of  these,  which  is  intuition,  is,  he  says,  "  the  kind 
of  intellectual  sympathy  by  which  one  places  oneself 
within  an  object  in  order  to  coincide  with  what  is  unique 
in  it  and  therefore  inexpressible  "  (p.  6).  In  illustration, 
he  mentions  self-knowledge  :  "  there  is  one  reality,  at 
least,  which  we  all  seize  from  within,  by  intuition  and 
not  by  simple  analysis.  It  is  our  own  personality  in  its 
flowing  through  time — our  self  which  endures  "  (p.  8). 
The  rest  of  Bergson's  philosophy  consists  in  reporting, 
through  the  imperfect  medium  of  words,  the  knowledge 
gained  by  intuition,  and  the  consequent  complete  con- 
demnation of  all  the  pretended  knowledge  derived  from 
science  and  common  sense. 

This  procedure,  since  it  takes  sides  in  a  conflict  of 
instinctive  beliefs,  stands  in  need  of  justification  by 
proving  the  greater  trustworthiness  of  the  beliefs  on  one 
side  than  of  those  on  the  other.  Bergson  attempts  this 
justification  in  two  ways,  first  by  explaining  that  intellect 
is  a  purely  practical  faculty  to  secure  biological  success, 

1  Introduction  to  Metaphysics,  p.  i. 


MYSTICISM  AND   LOGIC  15 

secondly  by  mentioning  remarkable  feats  of  instinct  in 
animals  and  by  pointing  out  characteristics  of  the  world 
which,  though  intuition  can  apprehend  them,  are 
baffling  to  intellect  as  he  interprets  it. 

Of  Bergson's  theory  that  intellect  is  a  purely  practical 
faculty,  developed  in  the  struggle  for  survival,  and  not  a 
source  of  true  beliefs,  we  may  say,  first,  that  it  is  only 
through  intellect  that  we  know  of  the  struggle  for  sur- 
vival and  of  the  biological  ancestry  of  man  :  if  the  intel- 
lect is  misleading,  the  whole  of  this  merely  inferred  history 
is  presumably  untrue.    If,  on  the  other  hand,  we  agree 
with  him  in  thinking  that  evolution  took  place  as  Darwin 
believed,  then  it  is  not  only  intellect,  but  all  our  faculties, 
that  have  been  developed  under  the  stress  of  practical 
utility.    Intuition  is  seen  at  its  best  where  it  is  directly 
useful,  for  example  in  regard  to  other  people's  characters 
and  dispositions.    Bergson  apparently  holds  that  capacity, 
for  this  kind  of  knowledge  is  less  explicable  by  the 
struggle  for  existence  than,  for  example,  capacity  for 
pure  mathematics.     Yet  the  savage  deceived  by  false 
friendship  is  likely  to  pay  for  his  mistake  with  his  life  ; 
whereas  even  in  the  most  civilised  societies  men  are  not 
put  to  death  for  mathematical  incompetence.     All  the 
most  striking  of  his  instances  of  intuition  in  animals  have 
a  very  direct  survival  value.    The  fact  is,  of  course,  that 
both  intuition  and  intellect  have  been  developed  because 
they  are  useful,  and  that,  speaking  broadly,  they  are  use- 
ful when  they  give  truth  and  become  harmful  when  they 
give  falsehood.    Intellect,  in  civilised  man,  like  artistic 
capacity,  has  occasionally  been  developed  beyond  the 
point  where  it  is  useful  to  the  individual ;  intuition,  on 
the  other  hand,  seems  on  the  whole  to  diminish  as 
civilisation  increases.    It  is  greater,  as  a  rule,  in  children 
than  in  adults,  in  the  uneducated  than  in  the  educated. 


16  MYSTICISM   AND   LOGIC 

Probably  in  dogs  it  exceeds  anything  to  be  found  in 
human  beings.  But  those  who  see  in  these  facts  a  recom- 
mendation of  intuition  ought  to  return  to  running  wild 
in  the  woods,  dyeing  themselves  with  woad  and  living 
on  hips  and  haws. 

Let  us  next  examine  whether  intuition  possesses  any 
such  infallibility  as  Bergson  claims  for  it.  The  best 
instance  of  it,  according  to  him,  is  our  acquaintance  with 
ourselves ;  yet  self-knowledge  is  proverbially  rare  and 
difficult.  Most  men,  for  example,  have  in  their  nature 
meannesses,  vanities,  and  envies  of  which  they  are  quite 
unconscious,  though  even  their  best  friends  can  perceive 
them  without  any  difficulty.  It  is  true  that  intuition  has 
a  convincingness  which  is  lacking  to  intellect  :  while  it  is 
present,  it  is  almost  impossible  to  doubt  its  truth.  But 
if  it  should  appear,  on  examination,  to  be  at  least  as 
fallible  as  intellect,  its  greater  subjective  certainty  be- 
comes a  demerit,  making  it  only  the  more  irresistibly 
deceptive.  Apart  from  self-knowledge,  one  of  the  most 
notable  examples  of  intuition  is  the  knowledge  people 
believe  themselves  to  possess  of  those  with  whom  they 
are  in  love  :  the  wall  between  different  personalities 
seems  to  become  transparent,  and  people  think  they  see 
into  another  soul  as  into  their  own.  Yet  deception  in 
such  cases  is  constantly  practised  with  success  ;  and  even 
where  there  is  no  intentional  deception,  experience 
gradually  proves,  as  a  rule,  that  the  supposed  insight 
was  illusory,  and  that  the  slower  more  groping  methods 
of  the  intellect  are  in  the  long  run  more  reliable. 

Bergson  maintains  that  intellect  can  only  deal  with 
things  in  so  far  as  they  resemble  what  has  been  experi- 
enced in  the  past,  while  intuition  has  the  power  of  appre- 
hending the  uniqueness  and  novelty  that  always  belong 
to  each  fresh  moment.  That  there  is  something  unique 


MYSTICISM   AND   LOGIC  17 

and  new  at  every  moment,  is  certainly  true  ;  it  is  also  true 
that  this  cannot  be  fully  expressed  by  means  of  intel- 
lectual concepts.  Only  direct  acquaintance  can  give 
knowledge  of  what  is  unique  and  new.  But  direct  ac- 
quaintance of  this  kind  is  given  fully  in  sensation,  and 
does  not  require,  so  far  as  I  can  see,  any  special  faculty 
of  intuition  for  its  apprehension.  It  is  neither  intellect 
nor  intuition,  but  sensation,  that  supplies  new  data  ; 
but  when  the  data  are  new  in  any  remarkable  manner, 
intellect  is  much  more  capable  of  dealing  with  them  than 
intuition  would  be.  The  hen  with  a  brood  of  ducklings 
no  doubt  has  intuition  which  seems  to  place  her  inside 
them,  and  not  merely  to  know  them  analytically ;  but 
when  the  ducklings  take  to  the  water,  the  whole  apparent 
intuition  is  seen  to  be  illusory,  and  the  hen  is  left  helpless 
on  the  shore.  Intuition,  in  fact,  is  an  aspect  and  develop- 
ment of  instinct,  and,  like  all  instinct,  is  admirable  in 
those  customary  surroundings  which  have  moulded  the 
habits  of  the  animal  in  question,  but  totally  incompetent 
as  soon  as  the  surroundings  are  changed  in  a  way  which 
demands  some  non-habitual  mode  of  action. 

The  theoretical  understanding  of  the  world,  which  is 
the  aim  of  philosophy,  is  not  a  matter  of  great  practical 
importance  to  animals,  or  to  savages,  or  even  to  most 
civilised  men.  It  is  hardly  to  be  supposed,  therefore, 
that  the  rapid,  rough  and  ready  methods  of  instinct  or 
intuition  will  find  in  this  field  a  favourable  ground  for 
their  application.  It  is  the  older  kinds  of  activity,  which 
bring  out  our  kinship  with  remote  generations  of  animal 
and  semi-human  ancestors,  that  show  intuition  at  its 
best.  In  such  matters  as  self-preservation  and  love, 
intuition  will  act  sometimes  (though  not  always)  with  a 
swiftness  and  precision  which  are  astonishing  to  the 
critical  intellect.  But  philosophy  is  not  one  of  the 


i8  MYSTICISM   AND   LOGIC 

pursuits  which  illustrate  our  affinity  with  the  past :  it  is 
a  highly  refined,  highly  civilised  pursuit,  demanding,  for 
its  success,  a  certain  liberation  from  the  life  of  instinct, 
and  even,  at  times,  a  certain  aloofness  from  all  mundane 
hopes  and  fears.  It  is  not  in  philosophy,  therefore,  that 
we  can  hope  to  see  intuition  at  its  best.  On  the  contrary, 
since  the  true  objects  of  philosophy,  and  the  habit  of 
thought  demanded  for  their  apprehension,  are  strange, 
unusual,  and  remote,  it  is  here,  more  almost  than  any- 
where else,  that  intellect  proves  superior  to  intuition, 
and  that  quick  unanalysed  convictions  are  least  deserving 
of  uncritical  acceptance. 

In  advocating  the  scientific  restraint  and  balance,  as 
against  the  self-assertion  of  a  confident  reliance  upon 
intuition,  we  are  only  urging,  in  the  sphere  of  knowledge, 
that  largeness  of  contemplation,  that  impersonal  dis- 
interestedness, and  that  freedom  from  practical  pre- 
occupations which  have  been  inculcated  by  all  the  great 
religions  of  the  world.  Thus  our  conclusion,  however  it 
may  conflict  with  the  explicit  beliefs  of  many  mystics,  is, 
in  essence,  not  contrary  to  the  spirit  which  inspires  those 
beliefs,  but  rather  the  outcome  of  this  very  spirit  as 
applied  in  the  realm  of  thought. 


II.   UNITY  AND   PLURALITY 

One  of  the  most  convincing  aspects  of  the  mystic 
illumination  is  the  apparent  revelation  of  the  oneness  of 
all  things,  giving  rise  to  pantheism  in  religion  and  to 
monism  in  philosophy.  An  elaborate  logic,  beginning 
with  Parmenides,  and  culminating  in  Hegel  and  his 
followers,  has  been  gradually  developed,  to  prove  that 
the  universe  is  one  indivisible  Whole,  and  that  what 
seem  to  be  its  parts,  if  considered  as  substantial  and  self- 


MYSTICISM   AND   LOGIC  19 

existing,  are  mere  illusion.  The  conception  of  a  Reality 
quite  other  than  the  world  of  appearance,  a  reality  one, 
indivisible,  and  unchanging,  was  introduced  into  Western 
philosophy  by  Parmenides,  not,  nominally  at  least,  for 
mystical  or  religious  reasons,  but  on  the  basis  of  a  logical 
argument  as  to  the  impossibility  of  not-being,  and  most 
subsequent  metaphysical  systems  are  the  outcome  of 
this  fundamental  idea. 

The  logic  used  in  defence  of  mysticism  seems  to  be 
faulty  as  logic,  and  open  to  technical  criticisms,  which  I 
have  explained  elsewhere.  I  shall  not  here  repeat  these 
criticisms,  since  they  are  lengthy  and  difficult,  but  shall 
instead  attempt  an  analysis  of  the  state  of  mind  from 
which  mystical  logic  has  arisen. 

Belief  in  a  reality  quite  different  from  what  appears  to 
the  senses  arises  with  irresistible  force  in  certain  moods, 
which  are  the  source  of  most  mysticism,  and  of  most 
metaphysics.  While  such  a  mood  is  dominant,  the  need 
of  logic  is  not  felt,  and  accordingly  the  more  thorough- 
going mystics  do  not  employ  logic,  but  appeal  directly 
to  the  immediate  deliverance  of  their  insight.  But  such 
fully  developed  mysticism  is  rare  in  the  West.  When 
the  intensity  of  emotional  conviction  subsides,  a  man 
who  is  in  the  habit  of  reasoning  will  search  for  logical 
grounds  in  favour  of  the  belief  which  he  finds  in  himself. 
But  since  the  belief  already  exists,  he  will  be  very  hos- 
pitable to  any  ground  that  suggests  itself.  The  paradoxes 
apparently  proved  by  his  logic  are  really  the  paradoxes 
of  mysticism,  and  are  the  goal  which  he  feels  his  logic 
must  reach  if  it  is  to  be  in  accordance  with  insight.  The 
resulting  logic  has  rendered  most  philosophers  incapable 
of  giving  any  account  of  the  world  of  science  and  daily 
life.  If  they  had  been  anxious  to  give  such  an  account, 
they  would  probably  have  discovered  the  errors  of  their 


20  MYSTICISM   AND   LOGIC 

logic  ;  but  most  of  them  were  less  anxious  to  understand 
the  world  of  science  and  daily  life  than  to  convict  it  of 
unreality  in  the  interests  of  a  super-sensible  "  real  " 
world. 

It  is  in  this  way  that  logic  has  been  pursued  by  those  of 
the  great  philosophers  who  were  mystics.  But  since  they 
usually  took  for  granted  the  supposed  insight  of  the 
mystic  emotion,  their  logical  doctrines  were  presented 
with  a  certain  dryness,  and  were  believed  by  their  dis- 
ciples to  be  quite  independent  of  the  sudden  illumination 
from  which  they  sprang.  Nevertheless  their  origin  clung 
to  them,  and  they  remained — to  borrow  a  useful  word 
from  Mr.  Santayana — "  malicious  "  in  regard  to  the 
world  of  science  and  common  sense.  It  is  only  so  that 
we  can  account  for  the  complacency  with  which  philo- 
sophers have  accepted  the  inconsistency  of  their  doctrines 
with  all  the  common  and  scientific  facts  which  seem  best 
established  and  most  worthy  of  belief. 

The  logic  of  mysticism  shows,  as  is  natural,  the  defects 
which  are  inherent  in  anything  malicious.  The  impulse 
to  logic,  not  felt  while  the  mystic  mood  is  dominant, 
reasserts  itself  as  the  mood  fades,  but  with  a  desire  to 
retain  the  vanishing  insight,  or  at  least  to  prove  that  it 
was  insight,  and  that  what  seems  to  contradict  it  is  illu- 
sion. The  logic  which  thus  arises  is  not  quite  dis- 
interested or  candid,  and  is  inspired  by  a  certain  hatred 
of  the  daily  world  to  which  it  is  to  be  applied.  Such  an 
attitude  naturally  does  not  tend  to  the  best  results. 
Everyone  knows  that  to  read  an  author  simply  in  order 
to  refute  him  is  not  the  way  to  understand  him  ;  and  to 
read  the  book  of  Nature  with  a  conviction  that  it  is  all 
illusion  is  just  as  unlikely  to  lead  to  understanding.  If 
our  logic  is  to  find  the  common  world  intelligible,  it  must 
not  be  hostile,  but  must  be  inspired  by  a  genuine  accept- 


MYSTICISM   AND   LOGIC  21 

ance  such  as  is  not  usually  to  be  found  among  meta- 
physicians. 

III.    TIME 

The  unreality  of  time  is  a  cardinal  doctrine  of  many 
metaphysical  systems,  often  nominally  based,  as  already 
by  Parmenides,  upon  logical  arguments,  but  originally 
derived,  at  any  rate  in  the  founders  of  new  systems,  from 
the  certainty  which  is  born  in  the  moment  of  mystic 
insight.  As  a  Persian  Sufi  poet  says  : 

"  Past  and  future  are  what  veil  God  from  our  sight. 
Burn  up  both  of  them  with  fire  !    How  long 
Wilt  thou  be  partitioned  by  these  segments  as  a  reed  ?  "* 

The  belief  that  what  is  ultimately  real  must  be  im- 
mutable is  a  very  common  one  :  it  gave  rise  to  the  meta- 
physical notion  of  substance,  and  finds,  even  now,  a 
wholly  illegitimate  satisfaction  in  such  scientific  doctrines 
as  the  conservation  of  energy  and  mass. 

It  is  difficult  to  disentangle  the  truth  and  the  error  in 
this  view.  The  arguments  for  the  contention  that  time 
is  unreal  and  that  the  world  of  sense  is  illusory  must,  I 
think,  be  regarded  as  fallacious.  Nevertheless  there  is 
some  sense — easier  to  feel  than  to  state — in  which  time 
is  an  unimportant  and  superficial  characteristic  of  reality. 
Past  and  future  must  be  acknowledged  to  be  as  real  as 
the  present,  and  a  certain  emancipation  from  slavery  to 
time  is  essential  to  philosophic  thought.  The  importance 
of  time  is  rather  practical  than  theoretical,  rather  in 
relation  to  our  desires  than  in  relation  to  truth.  A  truer 
image  of  the  world,  I  think,  is  obtained  by  picturing 
things  as  entering  into  the  stream  of  time  from  an 
eternal  world  outside,  than  from  a  view  which  regards 
time  as  the  devouring  tyrant  of  all  that  is.  Both  in 

1  Whinfield's  translation  of  the  Masnavi  (irubner,  1887),  p.  34. 


22  MYSTICISM   AND   LOGIC 

thought  and  in  feeling,  even  though  time  be  real,  to  realise 
the  unimportance  of  time  is  the  gate  of  wisdom. 

That  this  is  the  case  may  be  seen  at  once  by  asking 
ourselves  why  our  feelings  towards  the  past  are  so 
different  from  our  feelings  towards  the  future.  The 
reason  for  this  difference  is  wholly  practical :  our  wishes 
can  affect  the  future  but  not  the  past,  the  future  is  to 
some  extent  subject  to  our  power,  while  the  past  is  un- 
alterably fixed.  But  every  future  will  some  day  be  past  : 
if  we  see  the  past  truly  now,  it  must,  when  it  was  still 
future,  have  been  just  what  we  now  see  it  to  be,  and  what 
is  now  future  must  be  just  what  we  shall  see  it  to  be 
when  it  has  become  past.  The  felt  difference  of  quality 
between  past  and  future,  therefore,  is  not  an  intrinsic 
difference,  but  only  a  difference  in  relation  to  us  :  to 
impartial  contemplation,  it  ceases  to  exist.  And  im- 
partiality of  contemplation  is,  in  the  intellectual  sphere, 
that  very  same  virtue  of  disinterestedness  which,  in  the 
sphere  of  action,  appears  as  justice  and  unselfishness. 
Whoever  wishes  to  see  the  world  truly,  to  rise  in  thought 
above  the  tyranny  of  practical  desires,  must  learn  to 
overcome  the  difference  of  attitude  towards  past  and 
future,  and  to  survey  the  whole  stream  of  time  in  one 
comprehensive  vision. 

The  kind  of  way  in  which,  as  it  seems  to  me,  time  ought 
not  to  enter  into  our  theoretic  philosophical  thought, 
may  be  illustrated  by  the  philosophy  which  has  become 
associated  with  the  idea  of  evolution,  and  which  is  ex- 
emplified by  Nietzsche,  pragmatism,  and  Bergson.  This 
philosophy,  on  the  basis  of  the  development  which  has 
led  from  the  lowest  forms  of  life  up  to  man,  sees  in  progress 
the  fundamental  law  of  the  universe,  and  thus  admits  the 
difference  between  earlier  and  later  into  the  very  citadel 
of  its  contemplative  outlook.  With  its  past  and  future 


MYSTICISM   AND   LOGIC  23 

history  of  the  world,  conjectural  as  it  is,  I  do  not  wish  to 
quarrel.  But  I  think  that,  in  the  intoxication  of  a  quick 
success,  much  that  is  required  for  a  true  understanding 
of  the  universe  has  been  forgotten.  Something  of 
Hellenism,  something,  too,  of  Oriental  resignation,  must 
be  combined  with  its  hurrying  Western  self-assertion 
before  it  can  emerge  from  the  ardour  of  youth  into  the 
mature  wisdom  of  manhood.  In  spite  of  its  appeals  to 
science,  the  true  scientific  philosophy,  I  think,  is  some- 
thing more  arduous  and  more  aloof,  appealing  to  less 
mundane  hopes,  and  requiring  a  severer  discipline  for  its 
successful  practice. 

Darwin's  Origin  of  Species  persuaded  the  world  that 
the  difference  between  different  species  of  animals  and 
plants  is  not  the  fixed  immutable  difference  that  it 
appears  to  be.  The  doctrine  of  natural  kinds,  which  had 
rendered  classification  easy  and  definite,  which  was 
enshrined  in  the  Aristotelian  tradition,  and  protected  by 
its  supposed  necessity  for  orthodox  dogma,  was  suddenly 
swept  away  for  ever  out  of  the  biological  world.  The 
difference  between  man  and  the  lower  animals,  which  to 
our  human  conceit  appears  enormous,  was  shown  to  be  a 
gradual  achievement,  involving  intermediate  being  who 
could  not  with  certainty  be  placed  either  within  or  with- 
out the  human  family.  The  sun  and  the  planets  had 
already  been  shown  by  Laplace  to  be  very  probably 
derived  from  a  primitive  more  or  less  undifferentiated 
nebula.  Thus  the  old  fixed  landmarks  became  wavering 
and  indistinct,  and  all  sharp  outlines  were  blurred. 
Things  and  species  lost  their  boundaries,  and  none  could 
say  where  they  began  or  where  they  ended. 

But  if  human  conceit  was  staggered  for  a  moment  by 
its  kinship  with  the  ape,  it  soon  found  a  way  to  reassert 
itself,  and  that  way  is  the  "  philosophy  "  of  evolution. 


24  MYSTICISM   AND   LOGIC 

A  process  which  led  from  the  amoeba  to  Man  appeared 
to  the  philosophers  to  be  obviously  a  progress — though 
whether  the  amoeba  would  agree  with  this  opinion  is  not 
known.  Hence  the  cycle  of  changes  which  science  had 
shown  to  be  the  probable  history  of  the  past  was  wel- 
comed as  revealing  a  law  of  development  towards  good 
in  the  universe — an  evolution  or  unfolding  of  an  idea 
slowly  embodying  itself  in  the  actual.  But  such  a  view, 
though  it  might  satisfy  Spencer  and  those  whom  we  may 
call  Hegelian  evolutionists,  could  not  be  accepted  as 
adequate  by  the  more  whole-hearted  votaries  of  change. 
An  ideal  to  which  the  world  continuously  approaches  is, 
to  these  minds,  too  dead  and  static  to  be  inspiring.  Not 
only  the  aspiration,  but  the  ideal  too,  must  change  and 
develop  with  the  course  of  evolution  :  there  must  be  no 
fixed  goal,  but  a  continual  fashioning  of  fresh  needs  by 
the  impulse  which  is  life  and  which  alone  gives  unity  to 
the  process. 

Life,  in  this  philosophy,  is  a  continuous  stream,  in 
which  all  divisions  are  artificial  and  unreal.  Separate 
things,  beginnings  and  endings,  are  mere  convenient 
fictions :  there  is  only  smooth  unbroken  transition. 
The  beliefs  of  to-day  may  count  as  true  to-day,  if  they 
carry  us  along  the  stream  ;  but  to-morrow  they  will  be 
false,  and  must  be  replaced  by  new  beliefs  to  meet  the 
new  situation.  All  our  thinking  consists  of  convenient 
fictions,  imaginary  congealings  of  the  stream  :  reality 
flows  on  in  spite  of  all  our  fictions,  and  though  it  can  be 
lived,  it  cannot  be  conceived  in  thought.  Somehow, 
without  explicit  statement,  the  assurance  is  slipped  in 
that  the  future,  though  we  cannot  foresee  it,  will  be 
better  than  the  past  or  the  present  :  the  reader  is  like 
the  child  which  expects  a  sweet  because  it  has  been  told 
to  open  its  mouth  and  shut  its  eyes.  Logic,  mathematics, 


MYSTICISM   AND   LOGIC  25 

physics  disappear  in  this  philosophy,  because  they  are 
too  "  static  "  ;  what  is  real  is  no  impulse  and  movement 
towards  a  goal  which,  like  the  rainbow,  recedes  as  we 
advance,  and  makes  every  place  different  when  it  reaches 
it  from  what  it  appeared  to  be  at  a  distance. 

I  do  not  propose  to  enter  upon  a  technical  examination 
of  this  philosophy.  I  wish  only  to  maintain  that  the 
motives  and  interests  which  inspire  it  are  so  exclusively 
practical,  and  the  problems  with  which  it  deals  are  so 
special,  that  it  can  hardly  be  regarded  as  touching  any 
of  the  questions  that,  to  my  mind,  constitute  genuine 
philosophy. 

The  predominant  interest  of  evolutionism  is  in  the 
question  of  human  destiny,  or  at  least  of  the  destiny  of 
Life.  It  is  more  interested  in  morality  and  happiness 
than  in  knowledge  for  its  own  sake.  It  must  be  admitted 
that  the  same  may  be  said  of  many  other  philosophies, 
and  that  a  desire  for  the  kind  of  knowledge  which  philo- 
sophy can  give  is  very  rare.  But  if  philosophy  is  to 
attain  truth,  it  is  necessary  first  and  foremost  that 
philosophers  should  acquire  the  disinterested  intellectual 
curiosity  which  characterises  the  genuine  man  of  science. 
Knowledge  concerning  the  future — which  is  the  kind  of 
knowledge  that  must  be  sought  if  we  are  to  know  about 
human  destiny — is  possible  within  certain  narrow  limits. 
It  is  impossible  to  say  how  much  the  limits  may  be  en- 
larged with  the  progress  of  science.  But  what  is  evident 
is  that  any  proposition  about  the  future  belongs  by  its 
subject-matter  to  some  particular  science,  and  is  to  be 
ascertained,  if  at  all,  by  the  methods  of  that  science. 
Philosophy  is  not  a  short  cut  to  the  same  kind  of  results  as 
those  of  the  other  sciences  :  if  it  is  to  be  a  genuine  study, 
it  must  have  a  province  of  its  own,  and  aim  at  results 
which  the  other  sciences  can  neither  prove  nor  disprove. 


26  MYSTICISM   AND   LOGIC 

Evolutionism,  in  basing  itself  upon  the  notion  of 
progress,  which  is  change  from  the  worse  to  the  better, 
allows  the  notion  of  time,  as  it  seems  to  me,  to  become 
its  tyrant  rather  than  its  servant,  and  thereby  loses  that 
impartiality  of  contemplation  which  is  the  source  of  all 
that  is  best  in  philosophic  thought  and  feeling.  Meta- 
physicians, as  we  saw,  have  frequently  denied  altogether 
the  reality  of  time.  I  do  not  wish  to  do  this  ;  I  wish 
only  to  preserve  the  mental  outlook  which  inspired  the 
denial,  the  attitude  which,  in  thought,  regards  the  past 
as  having  the  same  reality  as  the  present  and  the  same 
importance  as  the  future.  "In  so  far,"  says  Spinoza,1 
"  as  the  mind  conceives  a  thing  according  to  the  dictate 
of  reason,  it  will  be  equally  affected  whether  the  idea  is 
that  of  a  future,  past,  or  present  thing."  It  is  this  "  con- 
ceiving according  to  the  dictate  of  reason  "  that  I  find 
lacking  in  the  philosophy  which  is  based  on  evolution. 

IV.   GOOD  AND  EVIL 

Mysticism  maintains  that  all  evil  is  illusory,  and  some- 
times maintains  the  same  view  as  regards  good,  but  more 
often  holds  that  all  Reality  is  good.  Both  views  are  to 
be  found  in  Heraclitus  :  "  Good  and  ill  are  one,"  he  says, 
but  again,  "  To  God  all  things  are  fair  and  good  and  right, 
but  men  hold  some  things  wrong  and  some  right."  A 
similar  twofold  position  is  to  be  found  in  Spinoza,  but  he 
uses  the  word  "  perfection  "  when  he  means  to  speak  of 
the  good  that  is  not  merely  human.  "  By  reality  and 
perfection  I  mean  the  same  thing,"  he  says  ;  2  but  else- 
where we  find  the  definition  :  "  By  good  I  shall  mean  that 
which  we  certainly  know  to  be  useful  to  us."3  Thus 
perfection  belongs  to  Reality  in  its  own  nature,  but  good- 

1  Ethics,  Bk.  IV,  Prop.  LXII.  2  Ethics,  Pt.  II,  Df.  VI. 

»  Ib.,  Pt.  IV,  Df.  I. 


MYSTICISM    AND   LOGIC  27 

ness  is  relative  to  ourselves  and  our  needs,  and  disappears 
in  an  impartial  survey.  Some  such  distinction,  I  think, 
is  necessary  in  order  to  understand  the  ethical  outlook 
of  mysticism  :  there  is  a  lower  mundane  kind  of  good 
and  evil,  which  divides  the  world  of  appearance  into 
what  seem  to  be  conflicting  parts  ;  but  there  is  also  a 
higher,  mystical  kind  of  good,  which  belongs  to  Reality 
and  is  not  opposed  by  any  correlative  kind  of  evil. 

It  is  difficult  to  give  a  logically  tenable  account  of  this 
position  without  recognising  that  good  and  evil  are  sub- 
jective, that  what  is  good  is  merely  that  towards  which 
we  have  one  kind  of  feeling,  and  what  is  evil  is  merely 
that  towards  which  we  have  another  kind  of  feeling.  In 
our  active  life,  where  we  have  to  exercise  choice,  and  to 
prefer  this  to  that  of  two  possible  acts,  it  is  necessary  to 
have  a  distinction  of  good  and  evil,  or  at  least  of  better 
and  worse.  But  this  distinction,  like  everything  per- 
taining to  action,  belongs  to  what  mysticism  regards  as 
the  world  of  illusion,  if  only  because  it  is  essentially 
concerned  with  time.  In  our  contemplative  life,  where 
action  is  not  called  for,  it  is  possible  to  be  impartial,  and 
to  overcome  the  ethical  dualism  which  action  requires. 
So  long  as  we  remain  merely  impartial,  we  may  be  content 
to  say  that  both  the  good  and  the  evil  of  action  are 
illusions.  But  if,  as  we  must  do  if  we  have  the  mystic 
vision,  we  find  the  whole  world  worthy  of  love  and 
worship,  if  we  see 

"  The  earth,  and  every  common  sight.  .  .  . 
Apparell'd  in  celestial  light," 

we  shall  say  that  there  is  a  higher  good  than  that  of 
action,  and  that  this  higher  good  belongs  to  the  whole 
world  as  it  is  in  reality.  In  this  way  the  twofold  attitude 
and  the  apparent  vacillation  of  mysticism  are  explained 
and  justified. 


28  MYSTICISM   AND   LOGIC 

The  possibility  of  this  universal  love  and  joy  in  all 
that  exists  is  of  supreme  importance  for  the  conduct  and 
happiness  of  life,  and  gives  inestimable  value  to  the 
mystic  emotion,  apart  from  any  creeds  which  may  be 
built  upon  it.  But  if  we  are  not  to  be  led  into  false 
beliefs,  it  is  necessary  to  realise  exactly  what  the  mystic 
emotion  reveals.  It  reveals  a  possibility  of  human  nature 
— a  possibility  of  a  nobler,  happier,  freer  life  than  any 
that  can  be  otherwise  achieved.  But  it  does  not  reveal 
anything  about  the  non-human,  or  about  the  nature  of 
the  universe  in  general.  Good  and  bad,  and  even  the 
higher  good  that  mysticism  finds  everywhere,  are  the 
reflections  of  our  own  emotions  on  other  things,  not  part 
of  the  substance  of  things  as  they  are  in  themselves. 
And  therefore  an  impartial  contemplation,  freed  from  all 
pre-occupation  with  Self,  will  not  judge  things  good  or 
bad,  although  it  is  very  easily  combined  with  that  feeling 
of  universal  love  which  leads  the  mystic  to  say  that  the 
whole  world  is  good. 

The  philosophy  of  evolution,  through  the  notion  of 
progress,  is  bound  up  with  the  ethical  dualism  of  the 
worse  and  the  better,  and  is  thus  shut  out,  not  only  from 
the  kind  of  survey  which  discards  good  and  evil  alto- 
gether from  its  view,  but  also  from  the  mystical  belief  in 
the  goodness  of  everything.  In  this  way  the  distinction 
of  good  and  evil,  like  time,  becomes  a  tyrant  in  this 
philosophy,  and  introduces  into  thought  the  restless 
selectiveness  of  action.  Good  and  evil,  like  time,  are,  it 
would  seem,  not  general  or  fundamental  in  the  world  of 
thought,  but  late  and  highly  specialised  members  of  the 
intellectual  hierarchy. 

Although,  as  we  saw,  mysticism  can  be  interpreted  so 
as  to  agree  with  the  view  that  good  and  evil  are  not 
intellectually  fundamental,  it  must  be  admitted  that  here 


MYSTICISM  AND   LOGIC  29 

we  are  no  longer  in  verbal  agreement  with  most  of  the 
great  philosophers  and  religious  teachers  of  the  past.  I 
believe,  however,  that  the  elimination  of  ethical  con- 
siderations from  philosophy  is  both  scientifically  necessary 
and — though  this  may  seem  a  paradox — an  ethical 
advance.  Both  these  contentions  must  be  briefly 
defended. 

The  hope  of  satisfaction  to  our  more  human  desires — 
the  hope  of  demonstrating  that  the  world  has  this  or  that 
desirable  ethical  characteristic — is  not  one  which,  so  far 
as  I  can  see,  a  scientific  philosophy  can  do  anything 
whatever  to  satisfy.  The  difference  between  a  good  world 
and  a  bad  one  is  a  difference  in  the  particular  character- 
istics of  the  particular  things  that  exist  in  these  worlds  : 
it  is  not  a  sufficiently  abstract  difference  to  come  within 
the  province  of  philosophy.  Love  and  hate,  for  example, 
are  ethical  opposites,  but  to  philosophy  they  are  closely 
analogous  attitudes  towards  objects.  The  general  form 
and  structure  of  those  attitudes  towards  objects  which 
constitute  mental  phenomena  is  a  problem  for  philosophy, 
but  the  difference  between  love  and  hate  is  not  a  difference 
of  form  or  structure,  and  therefore  belongs  rather  to  the 
special  science  of  psychology  than  to  philosophy.  Thus 
the  ethical  interests  which  have  often  inspired  philo- 
sophers must  remain  in  the  background  :  some  kind  of 
ethical  interest  may  inspire  the  whole  study,  but  none 
must  obtrude  in  the  detail  or  be  expected  in  the  special 
results  which  are  sought. 

If  this  view  seems  at  first  sight  disappointing,  we  may 
remind  ourselves  that  a  similar  change  has  been  found 
necessary  in  all  the  other  sciences.  The  physicist  or 
chemist  is  not  now  required  to  prove  the  ethical  im- 
portance of  his  ions  or  atoms  ;  the  biologist  is  not 
expected  to  prove  the  utility  of  the  plants  or  animals 


30  MYSTICISM   AND   LOGIC 

which  he  dissects.  In  pre-scientific  ages  this  was  not  the 
case.  Astronomy,  for  example,  was  studied  because 
men  believed  in  astrology  :  it  was  thought  that  the 
movements  of  the  planets  had  the  most  direct  and  im- 
portant bearing  upon  the  lives  of  human  beings.  Pre- 
sumably, when  this  belief  decayed  and  the  disinterested 
study  of  astronomy  began,  many  who  had  found  astrology 
absorbingly  interesting  decided  that  astronomy  had  too 
little  human  interest  to  be  worthy  of  study.  Physics,  as 
it  appears  in  Plato's  Timaeus  for  example,  is  full  of  ethical 
notions  :  it  is  an  essential  part  of  its  purpose  to  show 
that  the  earth  is  worthy  of  admiration.  The  modern 
physicist,  on  the  contrary,  though  he  has  no  wish  to  deny 
that  the  earth  is  admirable,  is  not  concerned,  as  physicist, 
with  its  ethical  attributes  :  he  is  merely  concerned  to 
find  out  facts,  not  to  consider  whether  they  are  good  or 
bad.  In  psychology,  the  scientific  attitude  is  even  more 
recent  and  more  difficult  than  in  the  physical  sciences  : 
it  is  natural  to  consider  that  human  nature  is  either  good 
or  bad,  and  to  suppose  that  the  difference  between  good 
and  bad,  so  all-important  in  practice,  must  be  important 
in  theory  also.  It  is  only  during  the  last  century  that  an 
ethically  neutral  psychology  has  grown  up ;  and  here 
too,  ethical  neutrality  has  been  essential  to  scientific 
success. 

In  philosophy,  hitherto,  ethical  neutrality  has  been 
seldom  sought  and  hardly  ever  achieved.  Men  have 
remembered  their  wishes,  and  have  judged  philosophies 
in  relation  to  their  wishes.  Driven  from  the  particular 
sciences,  the  belief  that  the  notions  of  good  and  evil  must 
afford  a  key  to  the  understanding  of  the  world  has  sought 
a  refuge  in  philosophy.  But  even  from  this  last  refuge,  if 
philosophy  is  not  to  remain  a  set  of  pleasing  dreams,  this 
belief  must  be  driven  forth.  It  is  a  commonplace  that 


MYSTICISM   AND   LOGIC  31 

happiness  is  not  best  achieved  by  those  who  seek  it 
directly  ;  and  it  would  seem  that  the  same  is  true  of  the 
good.  In  thought,  at  any  rate,  those  who  forget  good 
and  evil  and  seek  only  to  know  the  facts  are  more  likely 
to  achieve  good  than  those  who  view  the  world  through 
the  distorting  medium  of  their  own  desires. 

We  are  thus  brought  back  to  our  seeming  paradox, 
that  a  philosophy  which  does  not  seek  to  impose  upon 
the  world  its  own  conceptions  of  good  and  evil  is  not  only 
more  likely  to  achieve  truth,  but  is  also  the  outcome  of  a 
higher  ethical  standpoint  than  one  which,  like  evolu- 
tionism and  most  traditional  systems,  is  perpetually 
appraising  the  universe  and  seeking  to  find  in  it  an 
embodiment  of  present  ideals.  In  religion,  and  in  every 
deeply  serious  view  of  the  world  and  of  human  destiny, 
there  is  an  element  of  submission,  a  realisation  of  the 
limits  of  human  power,  which  is  somewhat  lacking  in 
the  modern  world,  with  its  quick  material  successes  and 
its  insolent  belief  in  the  boundless  possibilities  of  progress. 
"  He  that  loveth  his  life  shall  lose  it  "  ;  and  there  is 
danger  lest,  through  a  too  confident  love  of  life,  life  itself 
should  lose  much  of  what  gives  it  its  highest  worth.  The 
submission  which  religion  inculcates  in  action  is  essen- 
tially the  same  in  spirit  as  that  which  science  teaches  in 
thought ;  and  the  ethical  neutrality  by  which  its  victories 
have  been  achieved  is  the  outcome  of  that  submission. 

The  good  which  it  concerns  us  to  remember  is  the  good 
which  it  lies  in  our  power  to  create — the  good  in  our  own 
lives  and  in  our  attitude  towards  the  world.  Insistence 
on  belief  in  an  external  realisation  of  the  good  is  a  form 
of  self-assertion,  which,  while  it  cannot  secure  the 
external  good  which  it  desires,  can  seriously  impair  the 
inward  good  which  lies  within  our  power,  and  destroy  that 
reverence  towards  fact  which  constitutes  both  what  is 


32  MYSTICISM   AND   LOGIC 

valuable  in  humility  and  what  is  fruitful  in  the  scientific 
temper. 

Human  beings  cannot,  of  course,  wholly  transcend 
human  nature  ;  something  subjective,  if  only  the  interest 
that  determines  the  direction  of  our  attention,  must 
remain  in  all  our  thought.  But  scientific  philosophy 
comes  nearer  to  objectivity  than  any  other  human 
pursuit,  and  gives  us,  therefore,  the  closest  constant  and 
the  most  intimate  relation  with  the  outer  world  that  it  is 
possible  to  achieve.  To  the  primitive  mind,  everything 
is  either  friendly  or  hostile  ;  but  experience  has  shown 
that  friendliness  and  hostility  are  not  the  conceptions  by 
which  the  world  is  to  be  understood.  Scientific  philo- 
sophy thus  represents,  though  as  yet  only  in  a  nascent 
condition,  a  higher  form  of  thought  than  any  pre-scientific 
belief  or  imagination,  and,  like  every  approach  to  self- 
transcendence,  it  brings  with  it  a  rich  reward  in  increase 
of  scope  and  breadth  and  comprehension.  Evolutionism, 
in  spite  of  its  appeals  to  particular  scientific  facts,  fails  to 
be  a  truly  scientific  philosophy  because  of  its  slavery  to 
time,  its  ethical  preoccupations,  and  its  predominant 
interest  in  our  mundane  concerns  and  destiny.  A  truly 
scientific  philosophy  will  be  more  humble,  more  piece- 
meal, more  arduous,  offering  less  glitter  of  outward 
mirage  to  flatter  fallacious  hopes,  but  more  indifferent 
to  fate,  and  more  capable  of  accepting  the  world  without 
the  tyrannous  imposition  of  our  human  and  temporary 
demands. 


II 

THE   PLACE   OF  SCIENCE   IN   A 
LIBERAL   EDUCATION 


SCIENCE,  to  the  ordinary  reader  of  newspapers,  is 
represented  by  a  varying  selection  of  sensational 
triumphs,  such  as  wireless  telegraphy  and  aeroplanes, 
radio-activity  and  the  marvels  of  modern  alchemy.  It 
is  not  of  this  aspect  of  science  that  I  wish  to  speak. 
Science,  in  this  aspect,  consists  of  detached  up-to-date 
fragments,  interesting  only  until  they  are  replaced  by 
something  newer  and  more  up-to-date,  displaying 
nothing  of  the  systems  of  patiently  constructed  know- 
ledge out  of  which,  almost  as  a  casual  incident,  have 
come  the  practically  useful  results  which  interest  the 
man  in  the  street.  The  increased  command  over  the 
forces  of  nature  which  is  derived  from  science  is  un- 
doubtedly an  amply  sufficient  reason  for  encouraging 
scientific  research,  but  this  reason  has  been  so  often 
urged  and  is  so  easily  appreciated  that  other  reasons, 
to  my  mind  quite  as  important,  are  apt  to  be  overlooked. 
It  is  with  these  other  reasons,  especially  with  the  in- 
trinsic value  of  a  scientific  habit  of  mind  in  forming  our 
outlook  on  the  world,  that  I  shall  be  concerned  in  what 
follows. 

The  instance  of  wireless  telegraphy  will  serve  to  illus- 
trate the  difference  between  the  two  points  of  view. 
Almost  all  the  serious  intellectual  labour  required  for  the 
D  33 


34  MYSTICISM   AND   LOGIC 

possibility  of  this  invention  is  due  to  three  men — 
Faraday,  Maxwell,  and  Hertz.  In  alternating  layers  of 
experiment  and  theory  these  three  men  built  up  the 
modern  theory  of  electromagnetism,  and  demonstrated 
the  identity  of  light  with  electromagnetic  waves.  The 
system  which  they  discovered  is  one  of  profound  intel- 
lectual interest,  bringing  together  and  unifying  an  end- 
less variety  of  apparently  detached  phenomena,  and 
displaying  a  cumulative  mental  power  which  cannot  but 
afford  delight  to  every  generous  spirit.  The  mechanical 
details  which  remained  to  be  adjusted  in  order  to  utilise 
their  discoveries  for  a  practical  system  of  telegraphy 
demanded,  no  doubt,  very  considerable  ingenuity,  but 
had  not  that  broad  sweep  and  that  universality  which 
could  give  them  intrinsic  interest  as  an  object  of  dis- 
interested contemplation. 

From  the  point  of  view  of  training  the  mind,  of  giving 
that  well-informed,  impersonal  outlook  which  constitutes 
culture  in  the  good  sense  of  this  much-misused  word,  it 
seems  to  be  generally  held  indisputable  that  a  literary 
education  is  superior  to  one  based  on  science.  Even  the 
warmest  advocates  of  science  are  apt  to  rest  their  claims 
on  the  contention  that  culture  ought  to  be  sacrificed  to 
utility.  Those  men  of  science  who  respect  culture,  when 
they  associate  with  men  learned  in  the  classics,  are  apt 
to  admit,  not  merely  politely,  but  sincerely,  a  certain 
inferiority  on  their  side,  compensated  doubtless  by  the 
services  which  science  renders  to  humanity,  but  none  the 
less  real.  And  so  long  as  this  attitude  exists  among  men 
of  science,  it  tends  to  verify  itself :  the  intrinsically 
valuable  aspects  of  science  tend  to  be  sacrificed  to  the 
merely  useful,  and  little  attempt  is  made  to  preserve  that 
leisurely,  systematic  survey  by  which  the  finer  quality 
of  mind  is  formed  and  nourished. 


SCIENCE   AND   CULTURE  35 

But  even  if  there  be,  in  present  fact,  any  such  in- 
feriority as  is  supposed  in  the  educational  value  of  science, 
this  is,  I  believe,  not  the  fault  of  science  itself,  but  the 
fault  of  the  spirit  in  which  science  is  taught.  If  its  full 
possibilities  were  realised  by  those  who  teach  it,  I  believe 
that  its  capacity  of  producing  those  habits  of  mind  which 
constitute  the  highest  mental  excellence  would  be  at 
least  as  great  as  that  of  literature,  and  more  particularly 
of  Greek  and  Latin  literature.  In  saying  this  I  have  no 
wish  whatever  to  disparage  a  classical  education.  I  have 
not  myself  enjoyed  its  benefits,  and  my  knowledge  of 
Greek  and  Latin  authors  is  derived  almost  wholly  from 
translations.  But  I  am  firmly  persuaded  that  the  Greeks 
fully  deserve  all  the  admiration  that  is  bestowed  upon 
them,  and  that  it  is  a  very  great  and  serious  loss  to  be 
unacquainted  with  their  writings.  It  is  not  by  attacking 
them,  but  by  drawing  attention  to  neglected  excellences 
in  science,  that  I  wish  to  conduct  my  argument. 

One  defect,  however,  does  seem  inherent  in  a  purely 
classical  education — namely,  a  too  exclusive  emphasis 
on  the  past.  By  the  study  of  what  is  absolutely  ended 
and  can  never  be  renewed,  a  habit  of  criticism  towards 
the  present  and  the  future  is  engendered.  The  qualities 
in  which  the  present  excels  are  qualities  to  which  the 
study  of  the  past  does  not  direct  attention,  and  to 
which,  therefore,  the  student  of  Greek  civilisation  may 
easily  become  blind.  In  what  is  new  and  growing 
there  is  apt  to  be  something  crude,  insolent,  even  a 
little  vulgar,  which  is  shocking  to  the  man  of  sensitive 
taste  ;  quivering  from  the  rough  contact,  he  retires  to 
the  trim  gardens  of  a  polished  past,  forgetting  that  they 
were  reclaimed  from  the  wilderness  by  men  as  rough 
and  earth-soiled  as  those  from  whom  he  shrinks  in  his 
own  day.  The  habit  of  being  unable  to  recognise  merit 


36  MYSTICISM   AND   LOGIC 

until  it  is  dead  is  too  apt  to  be  the  result  of  a  purely 
bookish  life,  and  a  culture  based  wholly  on  the  past  will 
seldom  be  able  to  pierce  through  everyday  surroundings 
to  the  essential  splendour  of  contemporary  things,  or  to 
the  hope  of  still  greater  splendour  in  the  future. 

"  My  eyes  saw  not  the  men  of  old  ; 
And  now  their  age  away  has  rolled. 
I  weep — to  think  I  shall  not  see 
The  heroes  of  posterity." 

So  says  the  Chinese  poet ;  but  such  impartiality  is  rare 
in  the  more  pugnacious  atmosphere  of  the  West,  where 
the  champions  of  past  and  future  fight  a  never-ending 
battle,  instead  of  combining  to  seek  out  the  merits  of 
both. 

This  consideration,  which  militates  not  only  against 
the  exclusive  study  of  the  classics,  but  against  every 
form  of  culture  which  has  become  static,  traditional,  and 
academic,  leads  inevitably  to  the  fundamental  ques- 
tion :  What  is  the  true  end  of  education  ?  But  before 
attempting  to  answer  this  question  it  will  be  well  to 
define  the  sense  in  which  we  are  to  use  the  word  "  educa- 
tion." For  this  purpose  I  shall  distinguish  the  sense  in 
which  I  mean  to  use  it  from  two  others,  both  perfectly 
legitimate,  the  one  broader  and  the  other  narrower  than 
the  sense  in  which  I  mean  to  use  the  word. 

In  the  broader  sense,  education  will  include  not  only 
what  we  learn  through  instruction,  but  all  that  we  learn 
through  personal  experience — the  formation  of  character 
through  the  education  of  life .  Of  this  aspect  of  education , 
vitally  important  as  it  is,  I  will  say  nothing,  since  its 
consideration  would  introduce  topics  quite  foreign  to  the 
question  with  which  we  are  concerned. 

In  the  narrower  sense,  education  may  be  confined  to 
instruction,  the  imparting  of  definite  information  on 


SCIENCE   AND   CULTURE  37 

various  subjects,  because  such  information,  in  and  for 
itself,  is  useful  in  daily  life.  Elementary  education — 
reading,  writing,  and  arithmetic — is  almost  wholly  of 
this  kind.  But  instruction,  necessary  as  it  is,  does  not 
per  se  constitute  education  in  the  sense  in  which  I  wish 
to  consider  it. 

Education,  in  the  sense  in  which  I  mean  it,  may  be 
defined  as  the  formation,  by  means  of  instruction,  of  certain 
mental  habits  and  a  certain  outlook  on  life  and  the  world. 
It  remains  to  ask  ourselves,  what  mental  habits,  and 
what  sort  of  outlook,  can  be  hoped  for  as  the  result  of 
instruction  ?  When  we  have  answered  this  question  we 
can  attempt  to  decide  what  science  has  to  contribute  to 
the  formation  of  the  habits  and  outlook  which  we  desire. 

Our  whole  life  is  built  about  a  certain  number — not  a 
very  small  number — of  primary  instincts  and  impulses. 
Only  what  is  in  some  way  connected  with  these  instincts 
and  impulses  appears  to  us  desirable  or  important ;  there 
is  no  faculty,  whether  "  reason  "  or  "  virtue  "  or  what- 
ever it  may  be  called,  that  can  take  our  active  life  and 
our  hopes  and  fears  outside  the  region  controlled  by 
these  first  movers  of  all  desire.  Each  of  them  is  like  a 
queen-bee,  aided  by  a  hive  of  workers  gathering  honey  ; 
but  when  the  queen  is  gone  the  workers  languish  and 
die,  and  the  cells  remain  empty  of  their  expected  sweet- 
ness. So  with  each  primary  impulse  in  civilised  man  : 
it  is  surrounded  and  protected  by  a  busy  swarm  of 
attendant  derivative  desires,  which  store  up  in  its  service 
whatever  honey  the  surrounding  world  affords.  But  if 
the  queen-impulse  dies,  the  death-dealing  influence, 
though  retarded  a  little  by  habit,  spreads  slowly  through 
all  the  subsidiary  impulses,  and  a  whole  tract  of  life 
becomes  inexplicably  colourless.  What  was  formerly 
full  of  zest,  and  so  obviously  worth  doing  that  it  raised 


38  MYSTICISM   AND   LOGIC 

no  questions,  has  now  grown  dreary  and  purposeless  : 
with  a  sense  of  disillusion  we  inquire  the  meaning  of  life, 
and  decide,  perhaps,  that  all  is  vanity.  The  search  for 
an  outside  meaning  that  can  compel  an  inner  response 
must  always  be  disappointed  :  all  "  meaning  "  must  be 
at  bottom  related  to  our  primary  desires,  and  when  they 
are  extinct  no  miracle  can  restore  to  the  world  the  value 
which  they  reflected  upon  it. 

The  purpose  of  education,  therefore,  cannot  be  to 
create  any  primary  impulse  which  is  lacking  in  the 
uneducated  ;  the  purpose  can  only  be  to  enlarge  the 
scope  of  those  that  human  nature  provides,  by  increasing 
the  number  and  variety  of  attendant  thoughts,  and  by 
showing  where  the  most  permanent  satisfaction  is  to  be 
found.  Under  the  impulse  of  a  Calvinistic  horror  of 
the  "  natural  man,"  this  obvious  truth  has  been  too 
often  misconceived  in  the  training  of  the  young ; 
"  nature  "  has  been  falsely  regarded  as  excluding  all 
that  is  best  in  what  is  natural,  and  the  endeavour  to 
teach  virtue  has  led  to  the  production  of  stunted  and 
contorted  hypocrites  instead  of  full-grown  human  beings. 
From  such  mistakes  in  education  a  better  psychology  or 
a  kinder  heart  is  beginning  to  preserve  the  present 
generation  ;  we  need,  therefore,  waste  no  more  words  on 
the  theory  that  the  purpose  of  education  is  to  thwart  or 
eradicate  nature. 

But  although  nature  must  supply  the  initial  force  of 
desire,  nature  is  not,  in  the  civilised  man,  the  spasmodic, 
fragmentary,  and  yet  violent  set  of  impulses  that  it  is 
in  the  savage.  Each  impulse  has  its  constitutional 
ministry  of  thought  and  knowledge  and  reflection, 
through  which  possible  conflicts  of  impulses  are  foreseen, 
and  temporary  impulses  are  controlled  by  the  unifying 
impulse  which  may  be  called  wisdom.  In  this  way 


SCIENCE   AND   CULTURE  39 

education  destroys  the  crudity  of  instinct,  and  increases 
through  knowledge  the  wealth  and  variety  of  the  indi- 
vidual's contacts  with  the  outside  world,  making  him 
no  longer  an  isolated  fighting  unit,  but  a  citizen  of  the 
universe,  embracing  distant  countries,  remote  regions  of 
space,  and  vast  stretches  of  past  and  future  within  the 
circle  of  his  interests.  It  is  this  simultaneous  softening 
in  the  insistence  of  desire  and  enlargement  of  its  scope 
that  is  the  chief  moral  end  of  education. 

Closely  connected  with  this  moral  end  is  the  more 
purely  intellectual  aim  of  education,  the  endeavour  to 
make  us  see  and  imagine  the  world  in  an  objective 
manner,  as  far  as  possible  as  it  is  in  itself,  and  not  merely 
through  the  distorting  medium  of  personal  desire.  The 
complete  attainment  of  such  an  objective  view  is  no 
doubt  an  ideal,  indefinitely  approachable,  but  not  actually 
and  fully  realisable.  Education,  considered  as  a  process 
of  forming  our  mental  habits  and  our  outlook  on  the 
world,  is  to  be  judged  successful  in  proportion  as  its  out- 
come approximates  to  this  ideal ;  in  proportion,  that  is 
to  say,  as  it  gives  us  a  true  view  of  our  place  in  society, 
of  the  relation  of  the  whole  human  society  to  its  non- 
human  environment,  and  of  the  nature  of  the  non- 
human  world  as  it  is  in  itself  apart  from  our  desires  and 
interests.  If  this  standard  is  admitted,  we, can  return 
to  the  consideration  of  science,  inquiring  how  far  science 
contributes  to  such  an  aim,  and  whether  it  is  in  any 
respect  superior  to  its  rivals  in  educational  practice. 


II 

Two  opposite  and  at  first  sight  conflicting  merits 
belong  to  science  as  against  literature  and  art.  The  one, 
which  is  not  inherently  necessary,  but  is  certainly  true 


40  MYSTICISM   AND   LOGIC 

at  the  present  day,  is  hopefulness  as  to  the  future  of 
human  achievement,  and  in  particular  as  to  the  useful 
work  that  may  be  accomplished  by  any  intelligent 
student.  This  merit  and  the  cheerful  outlook  which  it 
engenders  prevent  what  might  otherwise  be  the  de- 
pressing effect  of  another  aspect  of  science,  to  my  mind 
also  a  merit,  and  perhaps  its  greatest  merit — I  mean  the 
irrelevance  of  human  passions  and  of  the  whole  subjective 
apparatus  where  scientific  truth  is  concerned.  Each  of 
these  reasons  for  preferring  the  study  of  science  requires 
some  amplification.  Let  us  begin  with  the  first. 

In  the  study  of  literature  or  art  our  attention  is  per- 
petually riveted  upon  the  past :  the  men  of  Greece  or 
of  the  Renaissance  did  better  than  any  men  do  now  ;  the 
triumphs  of  former  ages,  so  far  from  facilitating  fresh 
triumphs  in  our  own  age,  actually  increase  the  diffi- 
culty of  fresh  triumphs  by  rendering  originality  harder 
of  attainment ;  not  only  is  artistic  achievement  not 
cumulative,  but  it  seems  even  to  depend  upon  a  certain 
freshness  and  naivete  of  impulse  and  vision  which  civilisa- 
tion tends  to  destroy.  Hence  comes,  to  those  who  have 
been  nourished  on  the  literary  and  artistic  productions 
of  former  ages,  a  certain  peevishness  and  undue  fas- 
tidiousness towards  the  present,  from  which  there 
seems  no  escape  except  into  the  deliberate  vandalism 
which  ignores  tradition  and  in  the  search  after  originality 
achieves  only  the  eccentric.  But  in  such  vandalism 
there  is  none  of  the  simplicity  and  spontaneity  out  of 
which  great  art  springs  :  theory  is  still  the  canker  in  its 
core,  and  insincerity  destroys  the  advantages  of  a  merely 
pretended  ignorance. 

The  despair  thus  arising  from  an  education  which 
suggests  no  pre-eminent  mental  activity  except  that  of 
artistic  creation  is  wholly  absent  from  an  education 


SCIENCE   AND  CULTURE  41 

which  gives  the  knowledge  of  scientific  method.  The 
discovery  of  scientific  method,  except  in  pure  mathe- 
matics, is  a  thing  of  yesterday ;  speaking  broadly,  we 
may  say  that  it  dates  from  Galileo.  Yet  already  it  has 
transformed  the  world,  and  its  success  proceeds  with 
ever-accelerating  velocity.  In  science  men  have  dis- 
covered an  activity  of  the  very  highest  value  in  which 
they  are  no  longer,  as  in  art,  dependent  for  progress 
upon  the  appearance  of  continually  greater  genius,  for 
in  science  the  successors  stand  upon  the  shoulders  of 
their  predecessors ;  where  one  man  of  supreme  genius 
has  invented  a  method,  a  thousand  lesser  men  can  apply 
it.  No  transcendent  ability  is  required  in  order  to  make 
useful  discoveries  in  science  ;  the  edifice  of  science  needs 
its  masons,  bricklayers,  and  common  labourers  as  well 
as  its  foremen,  master-builders,  and  architects.  In  art 
nothing  worth  doing  can  be  done  without  genius  ;  in 
science  even  a  very  moderate  capacity  can  contribute  to 
a  supreme  achievement. 

In  science  the  man  of  real  genius  is  the  man  who 
invents  a  new  method.  The  notable  discoveries  are 
often  made  by  his  successors,  who  can  apply  the  method 
with  fresh  vigour,  unimpaired  by  the  previous  labour  of 
perfecting  it ;  but  the  mental  calibre  of  the  thought 
required  for  their  work,  however  brilliant,  is  not  so  great 
as  that  required  by  the  first  inventor  of  the  method. 
There  are  in  science  immense  numbers  of  different 
methods,  appropriate  to  different  classes  of  problems ; 
but  over  and  above  them  all,  there  is  something  not 
easily  definable,  which  may  be  called  the  method  of 
science.  It  was  formerly  customary  to  identify  this 
with  the  inductive  method,  and  to  associate  it  with  the 
name  of  Bacon.  But  the  true  inductive  method  was 
not  discovered  by  Bacon,  and  the  true  method  of  science 


42  MYSTICISM   AND   LOGIC 

is  something  which  includes  deduction  as  much  as 
induction,  logic  and  mathematics  as  much  as  botany  and 
geology.  I  shall  not  attempt  the  difficult  task  of  stating 
what  the  scientific  method  is,  but  I  will  try  to  indicate 
the  temper  of  mind  out  of  which  the  scientific  method 
grows,  which  is  the  second  of  the  two  merits  that  were 
mentioned  above  as  belonging  to  a  scientific  education. 

The  kernel  of  the  scientific  outlook  is  a  thing  so  simple, 
so  obvious,  so  seemingly  trivial,  that  the  mention  of  it 
may  almost  excite  derision.  The  kernel  of  the  scientific 
outlook  is  the  refusal  to  regard  our  own  desires,  tastes, 
and  interests  as  affording  a  key  to  the  understanding  of 
the  world.  Stated  thus  baldly,  this  may  seem  no  more 
than  a  trite  truism.  But  to  remember  it  consistently  in 
matters  arousing  our  passionate  partisanship  is  by  no 
means  easy,  especially  where  the  available  evidence  is 
uncertain  and  inconclusive.  A  few  illustrations  will 
make  this  clear. 

Aristotle,  I  understand,  considered  that  the  stars 
must  move  in  circles  because  the  circle  is  the  most 
perfect  curve.  In  the  absence  of  evidence  to  the  con- 
trary, he  allowed  himself  to  decide  a  question  of  fact  by 
an  appeal  to  aesthetico-moral  considerations.  In  such 
a  case  it  is  at  once  obvious  to  us  that  this  appeal  was 
unjustifiable.  We  know  now  how  to  ascertain  as  a  fact 
the  way  in  which  the  heavenly  bodies  move,  and  we 
know  that  they  do  not  move  in  circles,  or  even  in 
accurate  ellipses,  or  in  any  other  kind  of  simply  de- 
scribable  curve.  This  may  be  painful  to  a  certain 
hankering  after  simplicity  of  pattern  in  the  universe, 
but  we  know  that  in  astronomy  such  feelings  are  irre- 
levant. Easy  as  this  knowledge  seems  now,  we  owe  it 
to  the  courage  and  insight  of  the  first  inventors  of  scien- 
tific method,  and  more  especially  of  Galileo. 


SCIENCE   AND  CULTURE  43 

We  may  take  as  another  illustration  Malthus's 
doctrine  of  population.  This  illustration  is  all  the  better 
for  the  fact  that  his  actual  doctrine  is  now  known  to  be 
largely  erroneous.  It  is  not  his  conclusions  that  are 
valuable,  but  the  temper  and  method  of  his  inquiry. 
As  everyone  knows,  it  was  to  him  that  Darwin  owed  an 
essential  part  of  his  theory  of  natural  selection,  and 
this  was  only  possible  because  Malthus's  outlook  was 
truly  scientific.  His  great  merit  lies  in  considering  man 
not  as  the  object  of  praise  or  blame,  but  as  a  part  of 
nature,  a  thing  with  a  certain  characteristic  behaviour- 
from  which  certain  consequences  must  follow.  If  the 
behaviour  is  not  quite  what  Malthus  supposed,  if  the 
consequences  are  not  quite  what  he  inferred,  that  may 
falsify  his  conclusions,  but  does  not  impair  the  value  of 
his  method.  The  objections  which  were  made  when  his 
doctrine  was  new — that  it  was  horrible  and  depressing, 
that  people  ought  not  to  act  as  he  said  they  did,  and  so 
on — were  all  such  as  implied  an  unscientific  attitude  of 
mind  ;  as  against  all  of  them,  his  calm  determination 
to  treat  man  as  a  natural  phenomenon  marks  an  im- 
portant advance  over  the  reformers  of  the  eighteenth 
century  and  the  Revolution. 

Under  the  influence  of  Darwinism  the  scientific  atti- 
tude towards  man  has  now  become  fairly  common,  and 
is  to  some  people  quite  natural,  though  to  most  it  is  still  a 
difficult  and  artificial  intellectual  contortion.  There  is, 
however,  one  study  which  is  as  yet  almost  wholly  un- 
touched by  the  scientific  spirit — I  mean  the  study  of 
philosophy.  Philosophers  and  the  public  imagine  that 
the  scientific  spirit  must  pervade  pages  that  bristle  with 
allusions  to  ions,  germ-plasms,  and  the  eyes  of  shell-fish. 
But  as  the  devil  can  quote  Scripture,  so  the  philosopher 
can  quote  science.  The  scientific  spirit  is  not  an  affair  of 


44  MYSTICISM   AND   LOGIC 

quotation,  of  externally  acquired  information,  any  more 
than  manners  are  an  affair  of  the  etiquette-book.  The 
scientific  attitude  of  mind  involves  a  sweeping  away  of 
all  other  desires  in  the  interests  of  the  desire  to  know — 
it  involves  suppression  of  hopes  and  fears,  loves  and 
hates,  and  the  whole  subjective  emotional  life,  until  we 
become  subdued  to  the  material,  able  to  see  it  frankly, 
without  preconceptions,  without  bias,  without  any  wish 
except  to  see  it  as  it  is,  and  without  any  belief  that  what 
it  is  must  be  determined  by  some  relation,  positive  or 
negative,  to  what  we  should  like  it  to  be,  or  to  what  we 
can  easily  imagine  it  to  be. 

Now  in  philosophy  this  attitude  of  mind  has  not  as 
yet  been  achieved.  A  certain  self-absorption,  not  per- 
sonal, but  human,  has  marked  almost  all  attempts  to 
conceive  the  universe  as  a  whole.  Mind,  or  some  aspect 
of  it — thought  or  will  or  sentience — has  been  regarded 
as  the  pattern  after  which  the  universe  is  to  be  con- 
ceived, for  no  better  reason,  at  bottom,  than  that  such 
a  universe  would  not  seem  strange,  and  would  give 
us  the  cosy  feeling  that  every  place  is  like  home.  To 
conceive  the  universe  as  essentially  progressive  or  essen- 
tially deteriorating,  for  example,  is  to  give  to  our  hopes 
and  fears  a  cosmic  importance  which  may,  of  course, 
be  justified,  but  which  we  have  as  yet  no  reason  to  suppose 
justified.  Until  we  have  learnt  to  think  of  it  in  ethically 
neutral  terms,  we  have  not  arrived  at  a  scientific  attitude 
in  philosophy  ;  and  until  we  have  arrived  at  such  an 
attitude,  it  is  hardly  to  be  hoped  that  philosophy  will 
achieve  any  solid  results. 

I  have  spoken  so  far  largely  of  the  negative  aspect  of  the 
scientific  spirit,  but  it  is  from  the  positive  aspect  that  its 
value  is  derived.  The  instinct  of  constructiveness,  which  is 
one  of  the  chief  incentives  to  artistic  creation,  can  find 


SCIENCE   AND  CULTURE  45 

in  scientific  systems  a  satisfaction  more  massive  than 
any  epic  poem.  Disinterested  curiosity,  which  is  the 
source  of  almost  all  intellectual  effort,  finds  with  aston- 
ished delight  that  science  can  unveil  secrets  which 
might  well  have  seemed  for  ever  undiscoverable.  The 
desire  for  a  larger  life  and  wider  interests,  for  an  escape 
from  private  circumstances,  and  even  from  the  whole 
recurring  human  cycle  of  birth  and  death,  is  fulfilled  by 
the  impersonal  cosmic  outlook  of  science  as  by  nothing 
else.  To  all  these  must  be  added,  as  contributing  to  the 
happiness  of  the  man  of  science,  the  admiration  of 
splendid  achievement,  and  the  consciousness  of  inestim- 
able utility  to  the  human  race.  A  life  devoted  to  science 
is  therefore  a  happy  life,  and  its  happiness  is  derived 
from  the  very  best  sources  that  are  open  to  dwellers  on 
this  troubled  and  passionate  planet. 


Ill 
A   FREE   MAN'S  WORSHIP1 

TO  Dr.  Faustus  in  his  study  Mephistopheles  told  the 
history  of  the  Creation,  saying  : 

"  The  endless  praises  of  the  choirs  of  angels  had  begun 
to  grow  wearisome ;  for,  after  all,  did  he  not  deserve 
their  praise  ?  Had  he  not  given  them  endless  joy  ? 
Would  it  not  be  more  amusing  to  obtain  undeserved 
praise,  to  be  worshipped  by  beings  whom  he  tortured  ? 
He  smiled  inwardly,  and  resolved  that  the  great  drama 
should  be  performed. 

"  For  countless  ages  the  hot  nebula  whirled  aimlessly 
through  space.  At  length  it  began  to  take  shape,  the 
central  mass  threw  off  planets,  the  planets  cooled,  boil- 
ing seas  and  burning  mountains  heaved  and  tossed, 
from  black  masses  of  cloud  hot  sheets  of  rain  deluged 
the  barely  solid  crust.  And  now  the  first  germ  of  life 
grew  in  the  depths  of  the  ocean,  and  developed  rapidly 
in  the  fructifying  warmth  into  vast  forest  trees,  huge 
ferns  springing  from  the  damp  mould,  sea  monsters 
breeding,  fighting,  devouring,  and  passing  away.  And 
from  the  monsters,  as  the  play  unfolded  itself,  Man  was 
born,  with  the  power  of  thought,  the  knowledge  of  good 
and  evil,  and  the  cruel  thirst  for  worship.  And  Man 
saw  that  all  is  passing  in  this  mad,  monstrous  world, 
that  all  is  struggling  to  snatch,  at  any  cost,  a  few  brief 
moments  of  life  before  Death's  inexorable  decree.  And 

1  Reprinted  from  the  Independent  Review,  December,  1903. 
46 


A   FREE   MAN'S   WORSHIP  47 

Man  said  :  '  There  is  a  hidden  purpose,  could  we  but 
fathom  it,  and  the  purpose  is  good  ;  for  we  must  rever- 
ence something,  and  in  the  visible  world  there  is  nothing 
worthy  of  reverence.'  And  Man  stood  aside  from  the 
struggle,  resolving  that  God  intended  harmony  to  come 
out  of  chaos  by  human  efforts.  And  when  he  followed 
the  instincts  which  God  had  transmitted  to  him  from 
his  ancestry  of  beasts  of  prey,  he  called  it  Sin,  and  asked 
God  to  forgive  him.  But  he  doubted  whether  he  could 
be  justly  forgiven,  until  he  invented  a  divine  Plan  by 
which  God's  wrath  was  to  have  been  appeased.  And 
seeing  the  present  was  bad,  he  made  it  yet  worse,  that 
thereby  the  future  might  be  better.  And  he  gave  God 
thanks  for  the  strength  that  enabled  him  to  forgo  even 
the  joys  that  were  possible.  And  God  smiled  ;  and 
when  he  saw  that  Man  had  become  perfect  in  renuncia- 
tion and  worship,  he  sent  another  sun  through  the  sky, 
which  crashed  into  Man's  sun  ;  and  all  returned  again 
to  nebula. 

'  Yes,'  he  murmured,  '  it  was  a  good  play  ;    I  will 
have  it  performed  again.'  ' 

Such,  in  outline,  but  even  more  purposeless,  more 
void  of  meaning,  is  the  world  which  Science  presents  for 
our  belief.  Amid  such  a  world,  if  anywhere,  our  ideals 
henceforward  must  find  a  home.  That  Man  is  the 
product  of  causes  which  had  no  prevision  of  the  end 
they  were  achieving  ;  that  his  origin,  his  growth,  his 
hopes  and  fears,  his  loves  and  his  beliefs,  are  but  the 
outcome  of  accidental  collocations  of  atoms  ;  that  no  fire, 
no  heroism,  no  intensity  of  thought  and  feeling,  can 
preserve  an  individual  life  beyond  the  grave ;  that  all 
the  labours  of  the  ages,  all  the  devotion,  all  the  inspira- 
tion, all  the  noonday  brightness  of  human  genius,  are 
destined  to  extinction  in  the  vast  death  of  the  solar 


48  MYSTICISM   AND   LOGIC 

system,  and  that  the  whole  temple  of  Man's  achieve- 
ment must  inevitably  be  buried  beneath  the  debris  of  a 
universe  in  ruins — all  these  things,  if  not  quite  beyond 
dispute,  are  yet  so  nearly  certain,  that  no  philosophy 
which  rejects  them  can  hope  to  stand.  Only  within 
the  scaffolding  of  these  truths,  only  on  the  firm  founda- 
tion of  unyielding  despair,  can  the  soul's  habitation 
henceforth  be  safely  built. 

How,  in  such  an  alien  and  inhuman  world,  can  so 
powerless  a  creature  as  Man  preserve  his  aspirations 
untarnished  ?  A  strange  mystery  it  is  that  Nature, 
omnipotent  but  blind,  in  the  revolutions  of  her  secular 
hurryings  through  the  abysses  of  space,  has  brought 
forth  at  last  a  child,  subject  still  to  her  power,  but 
gifted  with  sight,  with  knowledge  of  good  and  evil,  with 
the  capacity  of  judging  all  the  works  of  his  unthinking 
Mother.  In  spite  of  Death,  the  mark  and  seal  of  the 
parental  control,  Man  is  yet  free,  during  his  brief  years, 
to  examine,  to  criticise,  to  know,  and  in  imagination  to 
create.  To  him  alone,  in  the  world  with  which  he  is 
acquainted,  this  freedom  belongs ;  and  in  this  lies  his 
superiority  to  the  resistless  forces  that  control  his  out- 
ward life. 

The  savage,  like  ourselves,  feels  the  oppression  of  his 
impotence  before  the  powers  of  Nature ;  but  having  in 
himself  nothing  that  he  respects  more  than  Power,  he  is 
willing  to  prostrate  himself  before  his  gods,  without 
inquiring  whether  they  are  worthy  of  his  worship. 
Pathetic  and  very  terrible  is  the  long  history  of  cruelty 
and  torture,  of  degradation  and  human  sacrifice,  endured 
in  the  hope  of  placating  the  jealous  gods  :  surely,  the 
trembling  believer  thinks,  when  what  is  most  precious 
has  been  freely  given,  their  lust  for  blood  must  be  ap- 
peased, and  more  will  not  be  required.  The  religion  of 


A   FREE   MAN'S   WORSHIP  49 

Moloch — as  such  creeds  may  be  generically  called — is  in 
essence  the  cringing  submission  of  the  slave,  who  dare 
not,  even  in  his  heart,  allow  the  thought  that  his  master 
deserves  no  adulation.  Since  the  independence  of  ideals 
is  not  yet  acknowledged,  Power  may  be  freely  wor- 
shipped, and  receive  an  unlimited  respect,  despite  its 
wanton  infliction  of  pain. 

But  gradually,  as  morality  grows  bolder,  the  claim  of 
the  ideal  world  begins  to  be  felt ;  and  worship,  if  it  is 
not  to  cease,  must  be  given  to  gods  of  another  kind  than 
those  created  by  the  savage.  Some,  though  they  feel 
the  demands  of  the  ideal,  will  still  consciously  reject 
them,  still  urging  that  naked  Power  is  worthy  of  worship. 
Such  is  the  attitude  inculcated  in  God's  answer  to  Job 
out  of  the  whirlwind  :  the  divine  power  and  knowledge 
are  paraded,  but  of  the  divine  goodness  there  is  no  hint. 
Such  also  is  the  attitude  of  those  who,  in  our  own  day, 
base  their  morality  upon  the  struggle  for  survival,  main- 
taining that  the  survivors  are  necessarily  the  fittest. 
But  others,  not  content  with  an  answer  so  repugnant  to 
the  moral  sense,  will  adopt  the  position  which  we  have 
become  accustomed  to  regard  as  specially  religious, 
maintaining  that,  in  some  hidden  manner,  the  world  of 
fact  is  really  harmonious  with  the  world  of  ideals.  Thus 
Man  creates  God,  all-powerful  and  all-good,  the  mystic 
unity  of  what  is  and  what  should  be. 

But  the  world  of  fact,  after  all,  is  not  good  ;  and,  in 
submitting  our  judgment  to  it,  there  is  an  element  of 
slavishness  from  which  our  thoughts  must  be  purged. 
For  in  all  things  it  is  well  to  exalt  the  dignity  of  Man, 
by  freeing  him  as  far  as  possible  from  the  tyranny  of 
non-human  Power.  When  we  have  realised  that  Power 
is  largely  bad,  that  man,  with  his  knowledge  of  good  and 
evil,  is  but  a  helpless  atom  in  a  world  which  has  no  such 

£ 


So  MYSTICISM   AND  LOGIC 

knowledge,  the  choice  is  again  presented  to  us  :  Shall 
we  worship  Force,  or  shall  we  worship  Goodness  ?  Shall 
our  God  exist  and  be  evil,  or  shall  he  be  recognised  as 
the  creation  of  our  own  conscience  ? 

The  answer  to  this  question  is  very  momentous,  and 
affects  profoundly  our  whole  morality.  The  worship  of 
Force,  to  which  Carlyle  and  Nietzsche  and  the  creed  of 
Militarism  have  accustomed  us,  is  the  result  of  failure  to 
maintain  our  own  ideals  against  a  hostile  universe  :  it  is 
itself  a  prostrate  submission  to  evil,  a  sacrifice  of  our 
best  to  Moloch.  If  strength  indeed  is  to  be  respected, 
let  us  respect  rather  the  strength  of  those  who  refuse 
that  false  "  recognition  of  facts  "  which  fails  to  recog- 
nise that  facts  are  often  bad.  Let  us  admit  that,  in  the 
world  we  know,  there  are  many  things  that  would  be 
better  otherwise,  and  that  the  ideals  to  which  we  do  and 
must  adhere  are  not  realised  in  the  realm  of  matter.  Let 
us  preserve  our  respect  for  truth,  for  beauty,  for  the 
ideal  of  perfection  which  life  does  not  permit  us  to 
attain,  though  none  of  these  things  meet  with  the  ap- 
proval of  the  unconscious  universe.  If  Power  is  bad,  as 
it  seems  to  be,  let  us  reject  it  from  our  hearts.  In  this 
lies  Man's  true  freedom  :  in  determination  to  worship 
only  the  God  created  by  our  own  love  of  the  good,  to 
respect  only  the  heaven  which  inspires  the  insight  of  our 
best  moments.  In  action,  in  desire,  we  must  submit 
perpetually  to  the  tyranny  of  outside  forces  ;  but  in 
thought,  in  aspiration,  we  are  free,  free  from  our  fellow- 
men,  free  from  the  petty  planet  on  which  our  bodies 
impotently  crawl,  free  even,  while  we  live,  from  the 
tyranny  of  death.  Let  us  learn,  then,  that  energy  of 
faith  which  enables  us  to  live  constantly  in  the  vision  of 
the  good  ;  and  let  us  descend,  in  action,  into  the  world 
of  fact,  with  that  vision  always  before  us. 


A    FREE    MAN'S   WORSHIP  51 

When  first  the  opposition  of  fact  and  ideal  grows  fully 
visible,  a  spirit  of  fiery  revolt,  of  fierce  hatred  of  the  gods, 
seems  necessary  to  the  assertion  of  freedom.  To  defy 
with  Promethean  constancy  a  hostile  universe,  to  keep 
its  evil  always  in  view,  always  actively  hated,  to  refuse 
no  pain  that  the  malice  of  Power  can  invent,  appears  to 
be  the  duty  of  all  who  will  not  bow  before  the  inevitable. 
But  indignation  is  still  a  bondage,  for  it  compels  our 
thoughts  to  be  occupied  with  an  evil  world  ;  and  in  the 
fierceness  of  desire  from  which  rebellion  springs  there  is 
a  kind  of  self-assertion  which  it  is  necessary  for  the  wise 
to  overcome.  Indignation  is  a  submission  of  our  thoughts, 
but  not  of  our  desires  ;  the  Stoic  freedom  in  which 
wisdom  consists  is  found  in  the  submission  of  our  desires, 
but  not  of  our  thoughts.  From  the  submission  of  our 
desires  springs  the  virtue  of  resignation  ;  from  the  free- 
dom of  our  thoughts  springs  the  whole  world  of  art  and 
philosophy,  and  the  vision  of  beauty  by  which,  at  last, 
we  half  reconquer  the  reluctant  world.  But  the  vision 
of  beauty  is  possible  only  to  unfettered  contemplation, 
to  thoughts  not  weighted  by  the  load  of  eager  wishes  ; 
and  thus  Freedom  comes  only  to  those  who  no  longer 
ask  of  life  that  it  shall  yield  them  any  of  those  personal 
goods  that  are  subject  to  the  mutations  of  Time. 

Although  the  necessity  of  renunciation  is  evidence  of 
the  existence  of  evil,  yet  Christianity,  in  preaching  it, 
has  shown  a  wisdom  exceeding  that  of  the  Promethean 
philosophy  of  rebellion.  It  must  be  admitted  that,  of 
the  things  we  desire,  some,  though  they  prove  impossible, 
are  yet  real  goods  ;  others,  however,  as  ardently  longed 
for,  do  not  form  part  of  a  fully  purified  ideal.  The  belief 
that  what  must  be  renounced  is  bad,  though  sometimes 
false,  is  far  less  often  false  than  untamed  passion  sup- 
poses ;  and  the  creed  of  religion,  by  providing  a  reason 


52  MYSTICISM   AND   LOGIC 

for  proving  that  it  is  never  false,  has  been  the  means  of 
purifying  our  hopes  by  the  discovery  of  many  austere 
truths. 

But  there  is  in  resignation  a  further  good  element : 
even  real  goods,  when  they  are  unattainable,  ought  not 
to  be  fretfully  desired.  To  every  man  comes,  sooner  or 
later,  the  great  renunciation.  For  the  young,  there  is 
nothing  unattainable  ;  a  good  thing  desired  with  the 
whole  force  of  a  passionate  will,  and  yet  impossible,  is  to 
them  not  credible.  Yet,  by  death,  by  illness,  by  poverty, 
or  by  the  voice  of  duty,  we  must  learn,  each  one  of  us, 
that  the  world  was  not  made  for  us,  and  that,  however 
beautiful  may  be  the  things  we  crave,  Fate  may  never- 
theless forbid  them.  It  is  the  part  of  courage,  when  mis- 
fortune comes,  to  bear  without  repining  the  ruin  of  our 
hopes,  to  turn  away  our  thoughts  from  vain  regrets. 
This  degree  of  submission  to  Power  is  not  only  just  and 
right :  it  is  the  very  gate  of  wisdom. 

But  passive  renunciation  is  not  the  whole  of  wisdom  ; 
for  not  by  renunciation  alone  can  we  build  a  temple  for 
the  worship  of  our  own  ideals.  Haunting  foreshadowings 
of  the  temple  appear  in  the  realm  of  imagination,  in 
music,  in  architecture,  in  the  untroubled  kingdom  of 
reason,  and  in  the  golden  sunset  magic  of  lyrics,  where 
beauty  shines  and  glows,  remote  from  the  touch  of 
sorrow,  remote  from  the  fear  of  change,  remote  from  the 
failures  and  disenchantments  of  the  world  of  fact.  In 
the  contemplation  of  these  things  the  vision  of  heaven 
will  shape  itself  in  our  hearts,  giving  at  once  a  touch- 
stone to  judge  the  world  about  us,  and  an  inspiration  by 
which  to  fashion  to  our  needs  whatever  is  not  incapable 
of  serving  as  a  stone  in  the  sacred  temple. 

Except  for  those  rare  spirits  that  are  born  without  sin, 
there  is  a  cavern  of  darkness  to  be  traversed  before  that 


A   FREE    MAN'S   WORSHIP  53 

temple  can  be  entered.  The  gate  of  the  cavern  is  despair, 
and  its  floor  is  paved  with  the  gravestones  of  abandoned 
hopes.  There  Self  must  die  ;  there  the  eagerness,  the 
greed  of  untamed  desire  must  be  slain,  for  only  so  can 
the  soul  be  freed  from  the  empire  of  Fate.  But  out  of 
the  cavern  the  Gate  of  Renunciation  leads  again  to  the 
daylight  of  wisdom,  by  whose  radiance  a  new  insight,  a 
new  joy,  a  new  tenderness,  shine  forth  to  gladden  the 
pilgrim's  heart. 

When,  without  the  bitterness  of  impotent  rebellion, 
we  have  learnt  both  to  resign  ourselves  to  the  outward 
rule  of  Fate  and  to  recognise  that  the  non-human  world 
is  unworthy  of  our  worship,  it  becomes  possible  at  last 
so  to  transform  and  refashion  the  unconscious  universe, 
so  to  transmute  it  in  the  crucible  of  imagination,  that  a 
new  image  of  shining  gold  replaces  the  old  idol  of  clay. 
In  all  the  multiform  facts  of  the  world — in  the  visual 
shapes  of  trees  and  mountains  and  clouds,  in  the  events 
of  the  life  of  man,  even  in  the  very  omnipotence  of  Death 
— the  insight  of  creative  idealism  can  find  the  reflection 
of  a  beauty  which  its  own  thoughts  first  made.  In  this 
way  mind  asserts  its  subtle  mastery  over  the  thoughtless 
forces  of  Nature.  The  more  evil  the  material  with  which 
it  deals,  the  more  thwarting  to  untrained  desire,  the 
greater  is  its  achievement  in  inducing  the  reluctant  rock 
to  yield  up  its  hidden  treasures,  the  prouder  its  victory 
in  compelling  the  opposing  forces  to  swell  the  pageant  of 
its  triumph.  Of  all  the  arts,  Tragedy  is  the  proudest,  the 
most  triumphant ;  for  it  builds  its  shining  citadel  in  the 
very  centre  of  the  enemy's  country,  on  the  very  summit 
of  his  highest  mountain  ;  from  its  impregnable  watch- 
towers,  his  camps  and  arsenals,  his  columns  and  forts, 
are  all  revealed  ;  within  its  walls  the  free  life  continues, 
while  the  legions  of  Death  and  Pain  and  Despair,  and  all 


54  MYSTICISM   AND   LOGIC 

the  servile  captains  of  tyrant  Fate,  afford  the  burghers 
of  that  dauntless  city  new  spectacles  of  beauty.  Happy 
those  sacred  ramparts,  thrice  happy  the  dwellers  on  that 
all-seeing  eminence.  Honour  to  those  brave  warriors 
who,  through  countless  ages  of  warfare,  have  preserved 
for  us  the  priceless  heritage  of  liberty,  and  have  kept 
undented  by  sacrilegious  invaders  the  home  of  the  un- 
subdued. 

But  the  beauty  of  Tragedy  does  but  make  visible  a 
quality  which,  in  more  or  less  obvious  shapes,  is  present 
always  and  everywhere  in  life.  In  the  spectacle  of  Death, 
in  the  endurance  of  intolerable  pain,  and  in  the  irrevocable- 
ness  of  a  vanished  past,  there  is  a  sacredness,  an  over- 
powering awe,  a  feeling  of  the  vastness,  the  depth,  the 
inexhaustible  mystery  of  existence,  in  which,  as  by  some 
strange  marriage  of  pain,  the  sufferer  is  bound  to  the 
world  by  bonds  of  sorrow.  In  these  moments  of  insight, 
we  lose  all  eagerness  of  temporary  desire,  all  struggling 
and  striving  for  petty  ends,  all  care  for  the  little  trivial 
things  that,  to  a  superficial  view,  make  up  the  common 
life  of  day  by  day  ;  we  see,  surrounding  the  narrow  raft 
illumined  by  the  flickering  light  of  human  comradeship, 
the  dark  ocean  on  whose  rolling  waves  we  toss  for  a  brief 
hour  ;  from  the  great  night  without,  a  chill  blast  breaks 
in  upon  our  refuge  ;  all  the  loneliness  of  "humanity  amid 
hostile  forces  is  concentrated  upon  the  individual  soul, 
which  must  struggle  alone,  with  what  of  courage  it  can 
command,  against  the  whole  weight  of  a  universe  that 
cares  nothing  for  its  hopes  and  fears.  Victory,  in  this 
struggle  with  the  powers  of  darkness,  is  the  true  baptism 
into  the  glorious  company  of  heroes,  the  true  initiation 
into  the  overmastering  beauty  of  human  existence.  From 
that  awful  encounter  of  the  soul  with  the  outer  world, 
enunciation,  wisdom,  and  charity  are  born  ;  and  with 


A   FREE   MAN'S   WORSHIP  55 

their  birth  a  new  life  begins.  To  take  into  the  inmost 
shrine  of  the  soul  the  irresistible  forces  whose  puppets 
we  seem  to  be — Death  and  change,  the  irrevocableness 
of  the  past,  and  the  powerlessness  of  man  before 
the  blind  hurry  of  the  universe  from  vanity  to  vanity 
— to  feel  these  things  and  know  them  is  to  conquer 
them. 

This  is  the  reason  why  the  Past  has  such  magical 
power.  The  beauty  of  its  motionless  and  silent  pictures 
is  like  the  enchanted  purity  of  late  autumn,  when  the 
leaves,  though  one  breath  would  make  them  fall,  still 
glow  against  the  sky  in  golden  glory.  The  Past  does  not 
change  or  strive  ;  like  Duncan,  after  life's  fitful  fever  it 
sleeps  well ;  what  was  eager  and  grasping,  what  was 
petty  and  transitory,  has  faded  away,  the  things  that 
were  beautiful  and  eternal  shine  out  of  it  like  stars  in  the 
night.  Its  beauty,  to  a  soul  not  worthy  of  it,  is  un- 
endurable ;  but  to  a  soul  which  has  conquered  Fate  it  is 
the  key  of  religion. 

The  life  of  Man,  viewed  outwardly,  is  but  a  small 
thing  in  comparison  with  the  forces  of  Nature.  The 
slave  is  doomed  to  worship  Time  and  Fate  and  Death, 
because  they  are  greater  than  anything  he  finds  in  him- 
self, and  because  all  his  thoughts  are  of  things  which 
they  devour.  But,  great  as  they  are,  to  think  of  them 
greatly,  to  feel  their  passionless  splendour,  is  greater 
still.  And  such  thought  makes  us  free  men  ;  we  no 
longer  bow  before  the  inevitable  in  Oriental  subjection, 
but  we  absorb  it,  and  make  it  a  part  of  ourselves.  To 
abandon  the  struggle  for  private  happiness,  to  expel  all 
eagerness  of  temporary  desire,  to  burn  with  passion  for 
eternal  things — this  is  emancipation,  and  this  is  the  free 
man's  worship.  And  this  liberation  is  effected  by  a  con- 
templation of  Fate  ;  for  Fate  itself  is  subdued  by  the 


56  MYSTICISM   AND   LOGIC 

mind  which  leaves  nothing  to  be  purged  by  the  purifying 
fire  of  Time. 

United  with  his  fellow-men  by  the  strongest  of  all  ties, 
the  tie  of  a  common  doom,  the  free  man  finds  that  a  new 
vision  is  with  him  always,  shedding  over  every  daily 
task  the  light  of  love.  The  life  of  Man  is  a  long  march 
through  the  night,  surrounded  by  invisible  foes,  tortured 
by  weariness  and  pain,  towards  a  goal  that  few  can  hope 
to  reach,  and  where  none  may  tarry  long.  One  by  one, 
as  they  march,  our  comrades  vanish  from  our  sight, 
seized  by  the  silent  orders  of  omnipotent  Death.  Very 
brief  is  the  time  in  which  we  can  help  them,  in  which 
their  happiness  or  misery  is  decided.  Be  it  ours  to  shed 
sunshine  on  their  path,  to  lighten  their  sorrows  by  the 
balm  of  sympathy,  to  give  them  the  pure  joy  of  a  never- 
tiring  affection,  to  strengthen  failing  courage,  to  instil 
faith  in  hours  of  despair.  Let  us  not  weigh  in  grudging 
scales  their  merits  and  demerits,  but  let  us  think  only  of 
their  need — of  the  sorrows,  the  difficulties,  perhaps  the 
blindnesses,  that  make  the  misery  of  their  lives  ;  let  us 
remember  that  they  are  fellow-sufferers  in  the  same 
darkness,  actors  in  the  same  tragedy  with  ourselves. 
And  so,  when  their  day  is  over,  when  their  good  and 
their  evil  have  become  eternal  by  the  immortality  of  the 
past,  be  it  ours  to  feel  that,  where  they  suffered,  where 
they  failed,  no  deed  of  ours  was  the  cause  ;  but  wherever 
a  spark  of  the  divine  fire  kindled  in  their  hearts,  we  were 
ready  with  encouragement,  with  sympathy,  with  brave 
words  in  which  high  courage  glowed. 

Brief  and  powerless  is  Man's  life  ;  on  him  and  all  his 
race  the  slow,  sure  doom  falls  pitiless  and  dark.  Blind 
to  good  and  evil,  reckless  of  destruction,  omnipotent 
matter  rolls  on  its  relentless  way  ;  for  Man,  condemned 
to-day  to  lose  his  dearest,  to-morrow  himself  to  pass 


A   FREE   MAN'S   WORSHIP  57 

through  the  gate  of  darkness,  it  remains  only  to  cherish, 
ere  yet  the  blow  falls,  the  lofty  thoughts  that  ennoble 
his  little  day  ;  disdaining  the  coward  terrors  of  the  slave 
of  Fate,  to  worship  at  the  shrine  that  his  own  hands  have 
built ;  undismayed  by  the  empire  of  chance,  to  preserve 
a  mind  free  from  the  wanton  tyranny  that  rules  his  out- 
ward life  ;  proudly  defiant  of  the  irresistible  forces  that 
tolerate,  for  a  moment,  his  knowledge  and  his  condemna- 
tion, to  sustain  alone,  a  weary  but  unyielding  Atlas,  the 
world  that  his  own  ideals  have  fashioned  despite  the 
trampling  march  of  unconscious  power. 


IN  regard  to  every  form  of  human  activity  it  is  neces- 
sary that  the  question  should  be  asked  from  time  to 
time,  What  is  its  purpose  and  ideal  ?  In  what  way  does 
it  contribute  to  the  beauty  of  human  existence  ?  As 
respects  those  pursuits  which  contribute  only  remotely, 
by  providing  the  mechanism  of  life,  it  is  well  to  be 
reminded  that  not  the  mere  fact  of  living  is  to  be  desired, 
but  the  art  of  living  in  the  contemplation  of  great  things. 
Still  more  in  regard  to  those  avocations  which  have  no 
end  outside  themselves,  which  are  to  be  justified,  if  at  all, 
as  actually  adding  to  the  sum  of  the  world's  permanent 
possessions,  it  is  necessary  to  keep  alive  a  knowledge  of 
their  aims,  a  clear  prefiguring  vision  of  the  temple  in 
which  creative  imagination  is  to  be  embodied. 

The  fulfilment  of  this  need,  in  what  concerns  the 
studies  forming  the  material  upon  which  custom  has 
decided  to  train  the  youthful  mind,  is  indeed  sadly 
remote — so  remote  as  to  make  the  mere  statement  of 
such  a  claim  appear  preposterous.  Great  men,  fully 
alive  to  the  beauty  of  the  contemplations  to  whose 
service  their  lives  are  devoted,  desiring  that  others  may 
share  in  their  joys,  persuade  mankind  to  impart  to  the 
successive  generations  the  mechanical  knowledge  with- 
out which  it  is  impossible  to  cross  the  threshold.  Dry 
pedants  possess  themselves  of  the  privilege  of  instilling 
this  knowledge  :  they  forget  that  it  is  to  serve  but  as  a 

58 


THE  STUDY  OF   MATHEMATICS         59 

key  to  open  the  doors  of  the  temple  ;  though  they  spend 
their  lives  on  the  steps  leading  up  to  those  sacred  doors, 
they  turn  their  backs  upon  the  temple  so  resolutely  that 
its  very  existence  is  forgotten,  and  the  eager  youth,  who 
would  press  forward  to  be  initiated  to  its  domes  and 
arches,  is  bidden  to  turn  back  and  count  the  steps. 

Mathematics,  perhaps  more  even  than  the  study  of 
Greece  and  Rome,  has  suffered  from  this  oblivion  of  its 
due  place  in  civilisation.  Although  tradition  has  decreed 
that  the  great  bulk  of  educated  men  shall  know  at  least 
the  elements  of  the  subject,  the  reasons  for  which  the 
tradition  arose  are  forgotten,  buried  beneath  a  great 
rubbish-heap  of  pedantries  and  trivialities.  To  those 
who  inquire  as  to  the  purpose  of  mathematics,  the  usual 
answer  will  be  that  it  facilitates  the  making  of  machines, 
the  travelling  from  place  to  place,  and  the  victory  over 
foreign  nations,  whether  in  war  or  commerce.  If  it  be 
objected  that  these  ends — all  of  which  are  of  doubtful 
value — are  not  furthered  by  the  merely  elementary 
study  imposed  upon  those  who  do  not  become  expert 
mathematicians,  the  reply,  it  is  true,  will  probably  be 
that  mathematics  trains  the  reasoning  faculties.  Yet 
the  very  men  who  make  this  reply  are,  for  the  most  part, 
unwilling  to  abandon  the  teaching  of  definite  fallacies, 
known  to  be  such,  and  instinctively  rejected  by  the  un- 
sophisticated mind  of  every  intelligent  learner.  And  the 
reasoning  faculty  itself  is  generally  conceived,  by  those 
who  urge  its  cultivation,  as  merely  a  means  for  the  avoid- 
ance of  pitfalls  and  a  help  in  the  discovery  of  rules  for 
the  guidance  of  practical  life.  All  these  are  undeniably 
important  achievements  to  the  credit  of  mathematics  ; 
yet  it  is  none  of  these  that  entitles  mathematics  to  a  place 
in  every  liberal  education.  Plato,  we  know,  regarded  the 
contemplation  of  mathematical  truths  as  worthy  of  the 


60  MYSTICISM   AND   LOGIC 

Deity  ;  and  Plato  realised,  more  perhaps  than  any  other 
single  man,  what  those  elements  are  in  human  life  which 
merit  a  place  in  heaven.  There  is  in  mathematics,  he 
says,  "  something  which  is  necessary  and  cannot  be  set 
aside  .  .  .  and,  if  I  mistake  not,  of  divine  necessity  ;  for 
as  to  the  human  necessities  of  which  the  Many  talk  in 
this  connection,  nothing  can  be  more  ridiculous  than  such 
an  application  of  the  words.  Cleinias.  And  what  are  these 
necessities  of  knowledge,  Stranger,  which  are  divine  and 
not  human  ?  Athenian.  Those  things  without  some  use 
or  knowledge  of  which  a  man  cannot  become  a  God  to 
the  world,  nor  a  spirit,  nor  yet  a  hero,  nor  able  earnestly 
to  think  and  care  for  man  "  (Laws,  p.  SiS).1  Such  was 
Plato's  judgment  of  mathematics ;  but  the  mathe- 
maticians do  not  read  Plato,  while  those  who  read  him 
know  no  mathematics,  and  regard  his  opinion  upon  this 
question  as  merely  a  curious  aberration. 

Mathematics,  rightly  viewed,  possesses  not  only  truth, 
but  supreme  beauty — a  beauty  cold  and  austere,  like 
that  of  sculpture,  without  appeal  to  any  part  of  our 
weaker  nature,  without  the  gorgeous  trappings  of  paint- 
ing or  music,  yet  sublimely  pure,  and  capable  of  a  stern 
perfection  such  as  only  the  greatest  art  can  show.  The 
true  spirit  of  delight,  the  exaltation,  the  sense  of  being 
more  than  man,  which  is  the  touchstone  of  the  highest 
excellence,  is  to  be  found  in  mathematics  as  surely  as  in 
poetry.  What  is  best  in  mathematics  deserves  not  merely 
to  be  learnt  as  a  task,  but  to  be  assimilated  as  a  part  of 
daily  thought,  and  brought  again  and  again  before  the 
mind  with  ever-renewed  encouragement.  Real  life  is,  to 
most  men,  a  long  second-best,  a  perpetual  compromise 
between  the  ideal  and  the  possible ;  but  the  world  of 
pure  reason  knows  no  compromise,  no  practical  limita- 

1  This  passage  was  pointed  out  to  me  by  Professor  Gilbert  Murray. 


THE   STUDY  OF   MATHEMATICS         61 

tions,  no  barrier  to  the  creative  activity  embodying  in 
splendid  edifices  the  passionate  aspiration  after  the  per- 
fect from  which  all  great  work  springs.  Remote  from 
human  passions,  remote  even  from  the  pitiful  facts  of 
nature,  the  generations  have  gradually  created  an 
ordered  cosmos,  where  pure  thought  can  dwell  as  in  its 
natural  home,  and  where  one,  at  least,  of  our  nobler 
impulses  can  escape  from  the  dreary  exile  of  the  actual 
world. 

So  little,  however,  have  mathematicians  aimed  at 
beauty,  that  hardly  anything  in  their  work  has  had  this 
conscious  purpose.  Much,  owing  to  irrepressible  instincts, 
which  were  better  than  avowed  beliefs,  has  been  moulded 
by  an  unconscious  taste  ;  but  much  also  has  been  spoilt 
by  false  notions  of  what  was  fitting.  The  characteristic 
excellence  of  mathematics  is  only  to  be  found  where  the 
reasoning  is  rigidly  logical :  the  rules  of  logic  are  to 
mathematics  what  those  of  structure  are  to  architecture. 
In  the  most  beautiful  work,  a  chain  of  argument  is  pre- 
sented in  which  every  link  is  important  on  its  own 
account,  in  which  there  is  an  air  of  ease  and  lucidity 
throughout,  and  the  premises  achieve  more  than  would 
have  been  thought  possible,  by  means  which  appear 
natural  and  inevitable.  Literature  embodies  what  is 
general  in  particular  circumstances  whose  universal 
significance  shines  through  their  individual  dress  ;  but 
mathematics  endeavours  to  present  whatever  is  most 
general  in  its  purity,  without  any  irrelevant  trappings. 

How  should  the  teaching  of  mathematics  be  conducted 
so  as  to  communicate  to  the  learner  as  much  as  possible 
of  this  high  ideal  ?  Here  experience  must,  in  a  great 
measure,  be  our  guide  ;  but  some  maxims  may  result 
from  our  consideration  of  the  ultimate  purpose  to  be 
achieved. 


62  MYSTICISM   AND   LOGIC 

One  of  the  chief  ends  served  by  mathematics,  when 
rightly  taught,  is  to  awaken  the  learner's  belief  in  reason, 
his  confidence  in  the  truth  of  what  has  been  demon- 
strated, and  in  the  value  of  demonstration.  This  purpose 
is  not  served  by  existing  instruction  ;  but  it  is  easy  to 
see  ways  in  which  it  might  be  served.  At  present,  in 
what  concerns  arithmetic,  the  boy  or  girl  is  given  a  set 
of  rules,  which  present  themselves  as  neither  true  nor 
false,  but  as  merely  the  will  of  the  teacher,  the  way  in 
which,  for  some  unfathomable  reason,  the  teacher  prefers 
to  have  the  game  played.  To  some  degree,  in  a  study  of 
such  definite  practical  utility,  this  is  no  doubt  unavoid- 
able ;  but  as  soon  as  possible,  the  reasons  of  rules  should 
be  set  forth  by  whatever  means  most  readily  appeal  to 
the  childish  mind.  In  geometry,  instead  of  the  tedious 
apparatus  of  fallacious  proofs  for  obvious  truisms  which 
constitutes  the  beginning  of  Euclid,  the  learner  should 
be  allowed  at  first  to  assume  the  truth  of  everything 
obvious,  and  should  be  instructed  in  the  demonstrations 
of  theorems  which  are  at  once  startling  and  easily  verifi- 
able by  actual  drawing,  such  as  those  in  which  it  is  shown 
that  three  or  more  lines  meet  in  a  point.  In  this  way 
belief  is  generated ;  it  is  seen  that  reasoning  may  lead 
to  startling  conclusions,  which  nevertheless  the  facts  will 
verify ;  and  thus  the  instinctive  distrust  of  whatever  is 
abstract  or  rational  is  gradually  overcome.  Where 
theorems  are  difficult,  they  should  be  first  taught  as 
exercises  in  geometrical  drawing,  until  the  figure  has 
become  thoroughly  familiar  ;  it  will  then  be  an  agreeable 
advance  to  be  taught  the  logical  connections  of  the 
various  lines  or  circles  that  occur.  It  is  desirable  also 
that  the  figure  illustrating  a  theorem  should  be  drawn  in 
all  possible  cases  and  shapes,  that  so  the  abstract  relations 
with  which  geometry  is  concerned  may  of  themselves 


THE   STUDY   OF   MATHEMATICS         63 

emerge  as  the  residue  of  similarity  amid  such  great 
apparent  diversity.  In  this  way  the  abstract  demon- 
strations should  form  but  a  small  part  of  the  instruction, 
and  should  be  given  when,  by  familiarity  with  concrete 
illustrations,  they  have  come  to  be  felt  as  the  natural 
embodiment  of  visible  fact.  In  this  early  stage  proofs 
should  not  be  given  with  pedantic  fullness  ;  definitely 
fallacious  methods,  such  as  that  of  superposition,  should 
be  rigidly  excluded  from  the  first,  but  where,  without 
such  methods,  the  proof  would  be  very  difficult,  the 
result  should  be  rendered  acceptable  by  arguments  and 
illustrations  which  are  explicitly  contrasted  with  demon- 
strations. 

In  the  beginning  of  algebra,  even  the  most  intelligent 
child  finds,  as  a  rule,  very  great  difficulty.  The  use  of 
letters  is  a  mystery,  which  seems  to  have  no  purpose 
except  mystification.  It  is  almost  impossible,  at  first, 
not  to  think  that  every  letter  stands  for  some  particular 
number,  if  only  the  teacher  would  reveal  what  number  it 
stands  for.  The  fact  is,  that  in  algebra  the  mind  is  first 
taught  to  consider  general  truths,  truths  which  are  not 
asserted  to  hold  only  of  this  or  that  particular  thing,  but 
of  any  one  of  a  whole  group  of  things.  It  is  in  the  power 
of  understanding  and  discovering  such  truths  that  the 
mastery  of  the  intellect  over  the  whole  world  of  things 
actual  and  possible  resides  ;  and  ability  to  deal  with  the 
general  as  such  is  one  of  the  gifts  that  a  mathematical 
education  should  bestow.  But  how  little,  as  a  rule,  is 
the  teacher  of  algebra  able  to  explain  the  chasm  which 
divides  it  from  arithmetic,  and  how  little  is  the  learner 
assisted  in  his  groping  efforts  at  comprehension  !  Usually 
the  method  that  has  been  adopted  in  arithmetic  is  con- 
tinued :  rules  are  set  forth,  with  no  adequate  explanation 
of  their  grounds  ;  the  pupil  learns  to  use  the  rules  blindly, 


64  MYSTICISM   AND   LOGIC 

and  presently,  when  he  is  able  to  obtain  the  answer  that 
the  teacher  desires,  he  feels  that  he  has  mastered  the 
difficulties  of  the  subject.  But  of  inner  comprehension 
of  the  processes  employed  he  has  probably  acquired 
almost  nothing. 

When  algebra  has  been  learnt,  all  goes  smoothly  until 
we  reach  those  studies  in  which  the  notion  of  infinity  is 
employed — the  infinitesimal  calculus  and  the  whole  of 
higher  mathematics.  The  solution  of  the  difficulties 
which  formerly  surrounded  the  mathematical  infinite  is 
probably  the  greatest  achievement  of  which  our  own  age 
has  to  boast.  Since  the  beginnings  of  Greek  thought 
these  difficulties  have  been  known  ;  in  every  age  the  finest 
intellects  have  vainly  endeavoured  to  answer  the  appar- 
ently unanswerable  questions  that  had  been  asked  by 
Zeno  the  Eleatic.  At  last  Georg  Cantor  has  found  the 
answer,  and  has  conquered  for  the  intellect  a  new  and 
vast  province  which  had  been  given  over  to  Chaos  and 
old  Night.  It  was  assumed  as  self-evident,  until  Cantor 
and  Dedekind  established  the  opposite,  that  if,  from  any 
collection  of  things,  some  were  taken  away,  the  number 
of  things  left  must  always  be  less  than  the  original 
number  of  things.  This  assumption,  as  a  matter  of  fact, 
holds  only  of  finite  collections ;  and  the  rejection  of  it, 
where  the  infinite  is  concerned,  has  been  shown  to  remove 
all  the  difficulties  that  had  hitherto  baffled  human  reason 
in  this  matter,  and  to  render  possible  the  creation  of 
an  exact  science  of  the  infinite.  This  stupendous  fact 
ought  to  produce  a  revolution  in  the  higher  teaching 
of  mathematics  ;  it  has  itself  added  immeasurably  to 
the  educational  value  of  the  subject,  and  it  has  at  last 
given  the  means  of  treating  with  logical  precision  many 
studies  which,  until  lately,  were  wrapped  in  fallacy 
and  obscurity.  By  those  who  were  educated  on  the 


THE   STUDY  OF   MATHEMATICS         65 

old  lines,  the  new  work  is  considered  to  be  appallingly 
difficult,  abstruse,  and  obscure  ;  and  it  must  be  con- 
fessed that  the  discoverer,  as  is  so  often  the  case,  has 
hardly  himself  emerged  from  the  mists  which  the  light 
of  his  intellect  is  dispelling.  But  inherently,  the  new 
doctrine  of  the  infinite,  to  all  candid  and  inquiring 
minds,  has  facilitated  the  mastery  of  higher  mathematics  ; 
for  hitherto,  it  has  been  necessary  to  learn,  by  a  long 
process  of  sophistication,  to  give  assent  to  arguments 
which,  on  first  acquaintance,  were  rightly  judged  to  be 
confused  and  erroneous.  So  far  from  producing  a  fear- 
less belief  in  reason,  a  bold  rejection  of  whatever  failed 
to  fulfil  the  strictest  requirements  of  logic,  a  mathematical 
training,  during  the  past  two  centuries,  encouraged  the 
belief  that  many  things,  which  a  rigid  inquiry  would 
reject  as  fallacious,  must  yet  be  accepted  because  they 
work  in  what  the  mathematician  calls  "  practice."  By 
this  means,  a  timid,  compromising  spirit,  or  else  a  sacer- 
dotal belief  in  mysteries  not  intelligible  to  the  profane, 
has  been  bred  where  reason  alone  should  have  ruled.  All 
this  it  is  now  time  to  sweep  away  ;  let  those  who  wish  to 
penetrate  into  the  arcana  of  mathematics  be  taught  at 
once  the  true  theory  in  all  its  logical  purity,  and  in  the 
concatenation  established  by  the  very  essence  of  the 
entities  concerned. 

If  we  are  considering  mathematics  as  an  end  in  itself, 
and  not  as  a  technical  training  for  engineers,  it  is  very 
desk-able  to  preserve  the  purity  and  strictness  of  its 
reasoning.  Accordingly  those  who  have  attained  a 
sufficient  familiarity  with  its  easier  portions  should  be 
led  backward  from  propositions  to  which  they  have 
assented  as  self-evident  to  more  and  more  fundamental 
principles  from  which  what  had  previously  appeared  as 
premises  can  be  deduced.  They  should  be  taught — 


66  MYSTICISM   AND   LOGIC 

what  the  theory  of  infinity  very  aptly  illustrates — that 
many  propositions  seem  self-evident  to  the  untrained 
mind  which,  nevertheless,  a  nearer  scrutiny  shows  to  be 
false.  By  this  means  they  will  be  led  to  a  sceptical 
inquiry  into  first  principles,  an  examination  of  the 
foundations  upon  which  the  whole  edifice  of  reasoning  is 
built,  or,  to  take  perhaps  a  more  fitting  metaphor,  the 
great  trunk  from  which  the  spreading  branches  spring. 
At  this  stage,  it  is  well  to  study  afresh  the  elementary 
portions  of  mathematics,  asking  no  longer  merely  whether 
a  given  proposition  is  true,  but  also  how  it  grows  out  of 
the  central  principles  of  logic.  Questions  of  this  nature 
can  now  be  answered  with  a  precision  and  certainty 
which  were  formerly  quite  impossible  ;  and  in  the  chains 
of  reasoning  that  the  answer  requires  the  unity  of  all 
mathematical  studies  at  last  unfolds  itself. 

In  the  great  majority  of  mathematical  text-books  there 
is  a  total  lack  of  unity  in  method  and  of  systematic 
development  of  a  central  theme.  Propositions  of  very 
diverse  kinds  are  proved  by  whatever  means  are  thought 
most  easily  intelligible,  and  much  space  is  devoted  to 
mere  curiosities  which  in  no  way  contribute  to  the  main 
argument.  But  in  the  greatest  works,  unity  and  in- 
evitability are  felt  as  in  the  unfolding  of  a  drama  ;  in  the 
premisses  a  subject  is  proposed  for  consideration,  and  in 
every  subsequent  step  some  definite  advance  is  made 
towards  mastery  of  its  nature.  The  love  of  system,  of 
interconnection,  which  is  perhaps  the  inmost  essence  of 
the  intellectual  impulse,  can  find  free  play  in  mathematics 
as  nowhere  else.  The  learner  who  feels  this  impulse 
must  not  be  repelled  by  an  array  of  meaningless  examples 
or  distracted  by  amusing  oddities,  but  must  be  encouraged 
to  dwell  upon  central  principles,  to  become  familiar  with 
the  structure -of  the  various  subjects  which  are  put  before 


THE  STUDY  OF   MATHEMATICS         67 

him,  to  travel  easily  over  the  steps  of  the  more  important 
deductions.  In  this  way  a  good  tone  of  mind  is  cultivated, 
and  selective  attention  is  taught  to  dwell  by  preference 
upon  what  is  weighty  and  essential. 

When  the  separate  studies  into  which  mathematics  is 
divided  have  each  been  viewed  as  a  logical  whole,  as  a 
natural  growth  from  the  propositions  which  constitute 
their  principles,  the  learner  will  be  able  to  understand 
the  fundamental  science  which  unifies  and  systematises 
the  whole  of  deductive  reasoning.  This  is  symbolic  logic 
— a  study  which,  though  it  owes  its  inception  to  Aristotle, 
is  yet,  in  its  wider  developments,  a  product,  almost 
wholly,  of  the  nineteenth  century,  and  is  indeed,  in  the 
present  day,  still  growing  with  great  rapidity.  The  true 
method  of  discovery  in  symbolic  logic,  and  probably  also 
the  best  method  for  introducing  the  study  to  a  learner 
acquainted  with  other  parts  of  mathematics,  is  the 
analysis  of  actual  examples  of  deductive  reasoning,  with 
a  view  to  the  discovery  of  the  principles  employed.  These 
principles,  for  the  most  part,  are  so  embedded  in  our 
ratiocinative  instincts,  that  they  are  employed  quite  un- 
consciously, and  can  be  dragged  to  light  only  by  much 
patient  effort.  But  when  at  last  they  have  been  found, 
they  are  seen  to  be  few  in  number,  and  to  be  the  sole 
source  of  everything  in  pure  mathematics.  The  dis- 
covery that  all  mathematics  follows  inevitably  from  a 
small  collection  of  fundamental  laws  is  one  which  im- 
measurably enhances  the  intellectual  beauty  of  the  whole  ; 
to  those  who  have  been  oppressed  by  the  fragmentary  and 
incomplete  nature  of  most  existing  chains  of  deduction 
this  discovery  comes  with  all  the  overwhelming  force  of  a 
revelation  ;  like  a  palace  emerging  from  the  autumn 
mist  as  the  traveller  ascends  an  Italian  hill-side,  the 
stately  storeys  of  the  mathematical  edifice  appear  in  their 


68  MYSTICISM   AND   LOGIC 

due  order  and  proportion,  with  a  new  perfection  in  every 
part. 

Until  symbolic  logic  had  acquired  its  present  develop- 
ment, the  principles  upon  which  mathematics  depends 
were  always  supposed  to  be  philosophical,  and  discover- 
able only  by  the  uncertain,  unprogressive  methods 
hitherto  employed  by  philosophers.  So  long  as  this  was 
thought,  mathematics  seemed  to  be  not  autonomous,  but 
dependent  upon  a  study  which  had  quite  other  methods 
than  its  own.  Moreover,  since  the  nature  of  the  postulates 
from  which  arithmetic,  analysis,  and  geometry  are  to  be 
deduced  was  wrapped  in  all  the  traditional  obscurities  of 
metaphysical  discussion,  the  edifice  built  upon  such 
dubious  foundations  began  to  be  viewed  as  no  better 
than  a  castle  in  the  air.  In  this  respect,  the  discovery 
that  the  true  principles  are  as  much  a  part  of  mathe- 
matics as  any  of  their  consequences  has  very  greatly 
increased  the  intellectual  satisfaction  to  be  obtained. 
This  satisfaction  ought  not  to  be  refused  to  learners 
capable  of  enjoying  it,  for  it  is  of  a  kind  to  increase  our 
respect  for  human  powers  and  our  knowledge  of  the 
beauties  belonging  to  the  abstract  world. 

Philosophers  have  commonly  held  that  the  laws  of 
logic,  which  underlie  mathematics,  are  laws  of  thought, 
laws  regulating  the  operations  of  our  minds.  By  this 
opinion  the  true  dignity  of  reason  is  very  greatly  lowered  ; 
it  ceases  to  be  an  investigation  into  the  very  heart  and 
immutable  essence  of  all  things  actual  and  possible,  be- 
coming, instead,  an  inquiry  into  something  more  or  less 
human  and  subject  to  our  limitations.  The  contemplation 
of  what  is  non-human,  the  discovery  that  our  minds  are 
capable  of  dealing  with  material  not  created  by  them, 
above  all,  the  realisation  that  beauty  belongs  to  the  outer 
world  as  to  the  inner,  are  the  chief  means  of  overcoming 


THE  STUDY  OF   MATHEMATICS         69 

the  terrible  sense  of  impotence,  of  weakness,  of  exile  amid 
hostile  powers,  which  is  too  apt  to  result  from  acknow- 
ledging the  ail-but  omnipotence  of  alien  forces.  To 
reconcile  us,  by  the  exhibition  of  its  awful  beauty,  to  the 
reign  of  Fate — which  is  merely  the  literary  personifica- 
tion of  these  forces — is  the  task  of  tragedy.  But  mathe- 
matics takes  us  still  further  from  what  is  human,  into  the 
region  of  absolute  necessity,  to  which  not  only  the  actual 
world,  but  every  possible  world,  must  conform ;  and 
even  here  it  builds  a  habitation,  or  rather  finds  a  habita- 
tion eternally  standing,  where  our  ideals  are  fully  satisfied 
and  our  best  hopes  are  not  thwarted.  It  is  only  when  we 
thoroughly  understand  the  entire  independence  of  our- 
selves, which  belongs  to  this  world  that  reason  finds,  that 
we  can  adequately  realise  the  profound  importance  of  its 
beauty. 

Not  only  is  mathematics  independent  of  us  and  our 
thoughts,  but  in  another  sense  we  and  the  whole  universe 
of  existing  things  are  independent  of  mathematics.  The 
apprehension  of  this  purely  ideal  character  is  indispens- 
able, if  we  are  to  understand  rightly  the  place  of 
mathematics  as  one  among  the  arts.  It  was  formerly  sup- 
posed that  pure  reason  could  decide,  in  some  respects,  as 
to  the  nature  of  the  actual  world  :  geometry,  at  least,  was 
thought  to  deal  with  the  space  in  which  we  live.  But  we 
now  know  that  pure  mathematics  can  never  pronounce 
upon  questions  of  actual  existence  :  the  world  of  reason, 
in  a  sense,  controls  the  world  of  fact,  but  it  is  not  at  any 
point  creative  of  fact,  and  in  the  application  of  its  results 
to  the  world  in  time  and  space,  its  certainty  and  precision 
are  lost  among  approximations  and  working  hypotheses. 
The  objects  considered  by  mathematicians  have,  in  the 
past,  been  mainly  of  a  kind  suggested  by  phenomena  ; 
but  from  such  restrictions  the  abstract  imagination 


70  MYSTICISM   AND   LOGIC 

should  be  wholly  free.  A  reciprocal  liberty  must  thus  be 
accorded  :  reason  cannot  dictate  to  the  world  of  facts, 
but  the  facts  cannot  restrict  reason's  privilege  of  dealing 
with  whatever  objects  its  love  of  beauty  may  cause  to 
seem  worthy  of  consideration.  Here,  as  elsewhere,  we 
build  up  our  own  ideals  out  of  the  fragments  to  be  found 
in  the  world  ;  and  in  the  end  it  is  hard  to  say  whether 
the  result  is  a  creation  or  a  discovery. 

It  is  very  desirable,  in  instruction,  not  merely  to  per- 
suade the  student  of  the  accuracy  of  important  theorems, 
but  to  persuade  him  in  the  way  which  itself  has,  of  all 
possible  ways,  the  most  beauty.  The  true  interest  of  a 
demonstration  is  not,  as  traditional  modes  of  exposition 
suggest,  concentrated  wholly  in  the  result ;  where  this 
does  occur,  it  must  be  viewed  as  a  defect,  to  be  remedied, 
if  possible,  by  so  generalising  the  steps  of  the  proof  that 
each  becomes  important  in  and  for  itself.  An  argument 
which  serves  only  to  prove  a  conclusion  is  like  a  story 
subordinated  to  some  moral  which  it  is  meant  to  teach  : 
for  aesthetic  perfection  no  part  of  the  whole  should  be 
merely  a  means.  A  certain  practical  spirit,  a  desire  for 
rapid  progress,  for  conquest  of  new  realms,  is  responsible 
for  the  undue  emphasis  upon  results  which  prevails  in 
mathematical  instruction.  The  better  way  is  to  propose 
some  theme  for  consideration — in  geometry,  a  figure 
having  important  properties ;  in  analysis,  a  function  of 
which  the  study  is  illuminating,  and  so  on.  Whenever 
proofs  depend  upon  some  only  of  the  marks  by  which  we 
define  the  object  to  be  studied,  these  marks  should  be 
isolated  and  investigated  on  their  own  account.  For  it 
is  a  defect,  in  an  argument,  to  employ  more  premisses 
than  the  conclusion  demands  :  what  mathematicians  call 
elegance  results  from  employing  only  the  essential  prin- 
ciples in  virtue  of  which  the  thesis  is  true.  It  is  a  merit  in 


THE   STUDY   OF   MATHEMATICS         71 

Euclid  that  he  advances  as  far  as  he  is  able  to  go  without 
employing  the  axiom  of  parallels — not,  as  is  often  said, 
because  this  axiom  is  inherently  objectionable,  but 
because,  in  mathematics,  every  new  axiom  diminishes 
the  generality  of  the  resulting  theorems,  and  the  greatest 
possible  generality  is  before  all  things  to  be  sought. 

Of  the  effects  of  mathematics  outside  its  own  sphere 
more  has  been  written  than  on  the  subject  of  its  own 
proper  ideal.  The  effect  upon  philosophy  has,  in  the 
past,  been  most  notable,  but  most  varied  ;  in  the  seven- 
teenth century,  idealism  and  rationalism,  in  the  eigh- 
teenth, materialism  and  sensationalism,  seemed  equally 
its  offspring.  Of  the  effect  which  it  is  likely  to  have  in 
the  future  it  would  be  very  rash  to  say  much  ;  but  in 
one  respect  a  good  result  appears  probable.  Against 
that  kind  of  scepticism  which  abandons  the  pursuit  of 
ideals  because  the  road  is  arduous  and  the  goal  not  cer- 
tainly attainable,  mathematics,  within  its  own  sphere,  is 
a  complete  answer.  Too  often  it  is  said  that  there  is  no 
absolute  truth,  but  only  opinion  and  private  judgment ; 
that  each  of  us  is  conditioned,  in  his  view  of  the  world, 
by  his  own  peculiarities,  his  own  taste  and  bias  ;  that 
there  is  no  external  kingdom  of  truth  to  which,  by  patience 
and  discipline,  we  may  at  last  obtain  admittance,  but  only 
truth  for  me,  for  you,  for  every  separate  person.  By  this 
habit  of  mind  one  of  the  chief  ends  of  human  effort  is 
denied,  and  the  supreme  virtue  of  candour,  of  fearless 
acknowledgment  of  what  is,  disappears  from  our  moral 
vision.  Of  such  scepticism  mathematics  is  a  perpetual 
reproof  ;  for  its  edifice  of  truths  stands  unshakable  and 
inexpugnable  to  all  the  weapons  of  doubting  cynicism. 

The  effects  of  mathematics  upon  practical  life,  though 
they  should  not  be  regarded  as  the  motive  of  our  studies, 
may  be  used  to  answer  a  doubt  to  which  the  solitary 


72  MYSTICISM   AND   LOGIC 

student  must  always  be  liable.  In  a  world  so  full  of  evil 
and  suffering,  retirement  into  the  cloister  of  contempla- 
tion, to  the  enjoyment  of  delights  which,  however  noble, 
must  always  be  for  the  few  only,  cannot  but  appear  as  a 
somewhat  selfish  refusal  to  share  the  burden  imposed 
upon  others  by  accidents  in  which  justice  plays  no  part. 
Have  any  of  us  the  right,  we  ask,  to  withdraw  from 
present  evils,  to  leave  our  fellow-men  unaided,  while  we 
live  a  life  which,  though  arduous  and  austere,  is  yet 
plainly  good  in  its  own  nature  ?  When  these  questions 
arise,  the  true  answer  is,  no  doubt,  that  some  must  keep 
alive  the  sacred  fire,  some  must  preserve,  in  every  genera- 
tion, the  haunting  vision  which  shadows  forth  the  goal  of 
so  much  striving.  But  when,  as  must  sometimes  occur, 
this  answer  seems  too  cold,  when  we  are  almost  maddened 
by  the  spectacle  of  sorrows  to  which  we  bring  no  help, 
then  we  may  reflect  that  indirectly  the  mathematician 
often  does  more  for  human  happiness  than  any  of  his 
more  practically  active  contemporaries.  The  history  of 
science  abundantly  proves  that  a  body  of  abstract  pro- 
positions— even  if,  as  in  the  case  of  conic  sections,  it 
remains  two  thousand  years  without  effect  upon  daily 
life — may  yet,  at  any  moment,  be  used  to  cause  a  revolu- 
tion in  the  habitual  thoughts  and  occupations  of  every 
citizen.  The  use  of  steam  and  electricity — to  take  striking 
instances — is  rendered  possible  only  by  mathematics.  In 
the  results  of  abstract  thought  the  world  possesses  a 
capital  of  which  the  employment  in  enriching  the  common 
round  has  no  hitherto  discoverable  limits.  Nor  does 
experience  give  any  means  of  deciding  what  parts  of 
mathematics  will  be  found  useful.  Utility,  therefore, 
can  be  only  a  consolation  in  moments  of  discouragement, 
not  a  guide  in  directing  our  studies. 

For  the  health  of  the  moral  life,  for  ennobling  the  tone 


THE   STUDY  OF  MATHEMATICS         73 

of  an  age  or  a  nation,  the  austerer  virtues  have  a  strange 
power,  exceeding  the  power  of  those  not  informed  and 
purified  by  thought.  Of  these  austerer  virtues  the  love  of 
truth  is  the  chief,  and  in  mathematics,  more  than  else- 
where, the  love  of  truth  may  find  encouragement  for  wan- 
ing faith.  Every  great  study  is  not  only  an  end  in  itself,  but 
also  a  means  of  creating  and  sustaining  a  lofty  habit  of 
mind  ;  and  this  purpose  should  be  kept  always  in  view 
throughout  the  teaching  and  learning  of  mathematics. 


MATHEMATICS  AND  THE 
METAPHYSICIANS 

THE  nineteenth  century,  which  prided  itself  upon 
the  invention  of  steam  and  evolution,  might  have 
derived  a  more  legitimate  title  to  fame  from  the  discovery 
of  pure  mathematics.  This  science,  like  most  others, 
was  baptised  long  before  it  was  born  ;  and  thus  we  find 
writers  before  the  nineteenth  century  alluding  to  what 
they  called  pure  mathematics.  But  if  they  had  been 
asked  what  this  subject  was,  they  would  only  have  been 
able  to  say  that  it  consisted  of  Arithmetic,  Algebra, 
Geometry,  and  so  on.  As  to  what  these  studies  had  in 
common,  and  as  to  what  distinguished  them  from  applied 
mathematics,  our  ancestors  were  completely  in  the  dark. 
Pure  mathematics  was  discovered  by  Boole,  in  a  work 
which  he  called  the  Laws  of  Thought  (1854).  This  work 
abounds  in  asseverations  that  it  is  not  mathematical, 
the  fact  being  that  Boole  was  too  modest  to  suppose  his 
book  the  first  ever  written  on  mathematics.  He  was  also 
mistaken  in  supposing  that  he  was  dealing  with  the  laws 
of  thought  :  the  question  how  people  actually  think  was 
quite  irrelevant  to  him,  and  if  his  book  had  really  con- 
tained the  laws  of  thought,  it  was  curious  that  no  one 
should  ever  have  thought  in  such  a  way  before.  His 
book  was  in  fact  concerned  with  formal  logic,  and  this 
is  the  same  thing  as  mathematics. 

74 


MATHEMATICS  AND  METAPHYSICIANS    75 

Pure  mathematics  consists  entirely  of  assertions  to  the 
effect  that,  if  such  and  such  a  proposition  is  true  of  any- 
thing, then  such  and  such  another  proposition  is  true  of 
that  thing.  It  is  essential  not  to  discuss  whether  the  first 
proposition  is  really  true,  and  not  to  mention  what  the 
anything  is,  of  which  it  is  supposed  to  be  true.  Both 
these  points  would  belong  to  applied  mathematics.  We 
start,  in  pure  mathematics,  from  certain  rules  of  infer- 
ence, by  which  we  can  infer  that  if  one  proposition  is 
true,  then  so  is  some  other  proposition.  These  rules  of 
inference  constitute  the  major  part  of  the  principles  of 
formal  logic.  We  then  take  any  hypothesis  that  seems 
amusing,  and  deduce  its  consequences,  //our  hypothesis 
is  about  anything,  and  not  about  some  one  or  more  particular 
things,  then  our  deductions  constitute  mathematics.  Thus 
mathematics  may  be  defined  as  the  subject  in  which  we 
never  know  what  we  are  talking  about,  nor  whether  what 
we  are  saying  is  true.  People  who  have  been  puzzled  by  the 
beginnings  of  mathematics  will,  I  hope,  find  comfort  in 
this  definition,  and  will  probably  agree  that  it  is  accurate. 

As  one  of  the  chief  triumphs  of  modern  mathematics 
consists  in  having  discovered  what  mathematics  really 
is,  a  few  more  words  on  this  subject  may  not  be  amiss. 
It  is  common  to  start  any  branch  of  mathematics — for 
instance,  Geometry — with  a  certain  number  of  primitive 
ideas,  supposed  incapable  of  definition,  and  a  certain 
number  of  primitive  propositions  or  axioms,  supposed 
incapable  of  proof.  Now  the  fact  is  that,  though  there 
are  indefinables  and  indemonstrables  in  every  branch  of 
applied  mathematics,  there  are  none  in  pure  mathematics 
except  such  as  belong  to  general  logic.  Logic,  broadly 
speaking,  is  distinguished  by  the  fact  that  its  propositions 
can  be  put  into  a  form  in  which  they  apply  to  anything 
whatever.  All  pure  mathematics — Arithmetic,  Analysis, 


76  MYSTICISM   AND   LOGIC 

and  Geometry — is  built  up  by  combinations  of  the  primi- 
tive ideas  of  logic,  and  its  propositions  are  deduced  from 
the  general  axioms  of  logic,  such  as  the  syllogism  and  the 
other  rules  of  inference.  And  this  is  no  longer  a  dream 
or  an  aspiration.  On  the  contrary,  over  the  greater  and 
more  difficult  part  of  the  domain  of  mathematics,  it  has 
been  already  accomplished  ;  in  the  few  remaining  cases, 
there  is  no  special  difficulty,  and  it  is  now  being  rapidly 
achieved.  Philosophers  have  disputed  for  ages  whether 
such  deduction  was  possible  ;  mathematicians  have  sat 
down  and  made  the  deduction.  For  the  philosophers 
there  is  now  nothing  left  but  graceful  acknowledg- 
ments. 

The  subject  of  formal  logic,  which  has  thus  at  last 
shown  itself  to  be  identical  with  mathematics,  was,  as 
every  one  knows,  invented  by  Aristotle,  and  formed  the 
chief  study  (other  than  theology)  of  the  Middle  Ages. 
But  Aristotle  never  got  beyond  the  syllogism,  which  is  a 
very  small  part  of  the  subject,  and  the  schoolmen  never 
got  beyond  Aristotle.  If  any  proof  were  required  of  our 
superiority  to  the  mediaeval  doctors,  it  might  be  found  in 
this.  Throughout  the  Middle  Ages,  almost  all  the  best 
intellects  devoted  themselves  to  formal  logic,  whereas  in 
the  nineteenth  century  only  an  infinitesimal  proportion  of 
the  world's  thought  went  into  this  subject.  Nevertheless, 
in  each  decade  since  1850  more  has  been  done  to  advance 
the  subject  than  in  the  whole  period  from  Aristotle  to 
Leibniz.  People  have  discovered  how  to  make  reasoning 
symbolic,  as  it  is  in  Algebra,  so  that  deductions  are 
effected  by  mathematical  rules.  They  have  discovered 
many  rules  besides  the  syllogism,  and  a  new  branch  of 
logic,  called  the  Logic  of  Relatives,1  has  been  invented 
to  deal  with  topics  that  wholly  surpassed  the  powers  of 
1  This  subject  is  due  in  the  main  to  Mr.  C.  S.  Peirce. 


MATHEMATICS  AND  METAPHYSICIANS     77 

the  old  logic,  though  they  form  the  chief  contents  of 
mathematics. 

It  is  not  easy  for  the  lay  mind  to  realise  the  importance 
of  symbolism  in  discussing  the  foundations  of  mathe- 
matics, and  the  explanation  may  perhaps  seem  strangely 
paradoxical.  The  fact  is  that  symbolism  is  useful  because 
it  makes  things  difficult.  (This  is  not  true  of  the  advanced 
parts  of  mathematics,  but  only  of  the  beginnings.)  What 
we  wish  to  know  is,  what  can  be  deduced  from  what. 
Now,  in  the  beginnings,  everything  is  self-evident ;  and 
it  is  very  hard  to  see  whether  one  self-evident  proposition 
follows  from  another  or  not.  Obviousness  is  always  the 
enemy  to  correctness.  Hence  we  invent  some  new  and 
difficult  symbolism,  in  which  nothing  seems  obvious. 
Then  we  set  up  certain  rules  for  operating  on  the  symbols, 
and  the  whole  thing  becomes  mechanical.  In  this  way 
we  find  out  what  must  be  taken  as  premiss  and  what  can 
be  demonstrated  or  defined.  For  instance,  the  whole  of 
Arithmetic  and  Algebra  has  been  shown  to  require  three 
indefinable  notions  and  five  indemonstrable  propositions. 
But  without  a  symbolism  it  would  have  been  very  hard 
to  find  this  out.  It  is  so  obvious  that  two  and  two  are  four, 
that  we  can  hardly  make  ourselves  sufficiently  sceptical 
to  doubt  whether  it  can  be  proved.  And  the  same  holds 
in  other  cases  where  self-evident  things  are  to  be  proved. 

But  the  proof  of  self-evident  propositions  may  seem,  to 
the  uninitiated,  a  somewhat  frivolous  occupation.  To 
this  we  might  reply  that  it  is  often  by  no  means  self- 
evident  that  one  obvious  proposition  follows  from  another 
obvious  proposition  ;  so  that  we  are  really  discovering 
new  truths  when  we  prove  what  is  evident  by  a  method 
which  is  not  evident.  But  a  more  interesting  retort  is, 
that  since  people  have  tried  to  prove  obvious  propositions, 
they  have  found  that  many  of  them  are  false.  Self- 


78  MYSTICISM   AND   LOGIC 

evidence  is  often  a  mere  will-o'-the-wisp,  which  is  sure  to 
lead  us  astray  if  we  take  it  as  our  guide.  For  instance, 
nothing  is  plainer  than  that  a  whole  always  has  more 
terms  than  a  part,  or  that  a  number  is  increased  by  add- 
ing one  to  it.  But  these  propositions  are  now  known  to 
be  usually  false.  Most  numbers  are  infinite,  and  if  a 
number  is  infinite  you  may  add  ones  to  it  as  long  as  you 
like  without  disturbing  it  in  the  least.  One  of  the  merits 
of  a  proof  is  that  it  instils  a  certain  doubt  as  to  the  result 
proved  ;  and  when  what  is  obvious  can  be  proved  in 
some  cases,  but  not  in  others,  it  becomes  possible  to  sup- 
pose that  in  these  other  cases  it  is  false. 

The  great  master  of  the  art  of  formal  reasoning,  among 
the  men  of  our  own  day,  is  an  Italian,  Professor  Peano, 
of  the  University  of  Turin.1  He  has  reduced  the  greater 
part  of  mathematics  (and  he  or  his  followers  will,  in  time, 
have  reduced  the  whole)  to  strict  symbolic  form,  in  which 
there  are  no  words  at  all.  In  the  ordinary  mathematical 
books,  there  are  no  doubt  fewer  words  than  most  readers 
would  wish.  Still,  little  phrases  occur,  such  as  therefore, 
let  us  assume,  consider,  or  hence  it  follows.  All  these,  how- 
ever, are  a  concession,  and  are  swept  away  by  Professor 
Peano.  For  instance,  if  we  wish  to  learn  the  whole  of 
Arithmetic,  Algebra,  the  Calculus,  and  indeed  all  that  is 
usually  called  pure  mathematics  (except  Geometry),  we 
must  start  with  a  dictionary  of  three  words.  One  symbol 
stands  for  zero,  another  for  number,  and  a  third  for  next 
after.  What  these  ideas  mean,  it  is  necessary  to  know  if 
you  wish  to  become  an  arithmetician.  But  after  symbols 
have  been  invented  for  these  three  ideas,  not  another 
word  is  required  in  the  whole  development.  All  future 
symbols  are  symbolically  explained  by  means  of  these 

1  I  ought  to  have  added  Frege,  but  his  writings  were  unknown  to 
me  when  this  article  was  written.  [Note  added  in  1917.] 


MATHEMATICS  AND  METAPHYSICIANS    79 

three.  Even  these  three  can  be  explained  by  means  of 
the  notions  of  relation  and  class  ;  but  this  requires  the 
Logic  of  Relations,  which  Professor  Peano  has  never 
taken  up.  It  must  be  admitted  that  what  a  mathe- 
matician has  to  know  to  begin  with  is  not  much.  There 
are  at  most  a  dozen  notions  out  of  which  all  the  notions 
in  all  pure  mathematics  (including  Geometry)  are  com- 
pounded. Professor  Peano,  who  is  assisted  by  a  very 
able  school  of  young  Italian  disciples,  has  shown  how 
this  may  be  done  ;  and  although  the  method  which  he 
has  invented  is  capable  of  being  carried  a  good  deal 
further  than  he  has  carried  it,  the  honour  of  the  pioneer 
must  belong  to  him. 

Two  hundred  years  ago,  Leibniz  foresaw  the  science 
which  Peano  has  perfected,  and  endeavoured  to  create  it. 
He  was  prevented  from  succeeding  by  respect  for  the 
authority  of  Aristotle,  whom  he  could  not  believe  guilty 
of  definite,  formal  fallacies  ;  but  the  subject  which  he 
desired  to  create  now  exists,  in  spite  of  the  patronising 
contempt  with  which  his  schemes  have  been  treated  by  all 
superior  persons.  From  this  "  Universal  Characteristic," 
as  he  called  it,  he  hoped  for  a  solution  of  all  problems, 
and  an  end  to  all  disputes.  "  If  controversies  were  to 
arise,"  he  says,  "  there  would  be  no  more  need  of  dis- 
putation between  two  philosophers  than  between  two 
accountants.  For  it  would  suffice  to  take  their  pens  in 
their  hands,  to  sit  down  to  their  desks,  and  to  say  to 
each  other  (with  a  friend  as  witness,  if  they  liked),  '  Let 
us  calculate.' '  This  optimism  has  now  appeared  to  be 
somewhat  excessive  ;  there  still  are  problems  whose 
solution  is  doubtful,  and  disputes  which  calculation 
cannot  decide.  But  over  an  enormous  field  of  what  was 
formerly  controversial,  Leibniz's  dream  has  become  sober 
fact.  In  the  whole  philosophy  of  mathematics,  which 


8o  MYSTICISM   AND   LOGIC 

used  to  be  at  least  as  full  of  doubt  as  any  other  part  of 
philosophy,  order  and  certainty  have  replaced  the  con- 
fusion and  hesitation  which  formerly  reigned.  Philo- 
sophers, of  course,  have  not  yet  discovered  this  fact,  and 
continue  to  write  on  such  subjects  in  the  old  way.  But 
mathematicians,  at  least  in  Italy,  have  now  the  power  of 
treating  the  principles  of  mathematics  in  an  exact  and 
masterly  manner,  by  means  of  which  the  certainty  of 
mathematics  extends  also  to  mathematical  philosophy. 
Hence  many  of  the  topics  which  used  to  be  placed  among 
the  great  mysteries — for  example,  the  natures  of  infinity, 
of  continuity,  of  space,  time  and  motion — are  now  no 
longer  in  any  degree  open  to  doubt  or  discussion.  Those 
who  wish  to  know  the  nature  of  these  things  need  only 
read  the  works  of  such  men  as  Peano  or  Georg  Cantor  ; 
they  will  there  find  exact  and  indubitable  expositions  of 
all  these  quondam  mysteries. 

In  this  capricious  world,  nothing  is  more  capricious 
than  posthumous  fame.  One  of  the  most  notable  examples 
of  posterity's  lack  of  judgment  is  the  Eleatic  Zeno.  This 
man,  who  may  be  regarded  as  the  founder  of  the  philo- 
sophy of  infinity,  appears  in  Plato's  Parmenides  in  the 
privileged  position  of  instructor  to  Socrates.  He  invented 
four  arguments,  all  immeasurably  subtle  and  profound, 
to  prove  that  motion  is  impossible,  that  Achilles  can 
never  overtake  the  tortoise,  and  that  an  arrow  in  flight 
is  really  at  rest.  After  being  refuted  by  Aristotle,  and 
by  every  subsequent  philosopher  from  that  day  to  our 
own,  these  arguments  were  reinstated,  and  made  the 
basis  of  a  mathematical  renaissance,  by  a  German  pro- 
fessor, who  probably  never  dreamed  of  any  connection 
between  himself  and  Zeno.  Weierstrass,1  by  strictly 

1  Professor  of  Mathematics  in  the  University  of  Berlin.  He  died  in 
1897. 


MATHEMATICS  AND  METAPHYSICIANS    81 

banishing  from  mathematics  the  use  of  infinitesimals, 
has  at  last  shown  that  we  live  in  an  unchanging  world, 
and  that  the  arrow  in  its  flight  is  truly  at  rest. 
Zeno's  only  error  lay  in  inferring  (if  he  did  infer) 
that,  because  there  is  no  such  thing  as  a  state  of 
change,  therefore  the  world  is  in  the  same  state 
at  any  one  time  as  at  any  other.  This  is  a  conse- 
quence which  by  no  means  follows  ;  and  in  this  respect, 
the  German  mathematician  is  more  constructive  than 
the  ingenious  Greek.  Weierstrass  has  been  able,  by 
embodying  his  views  in  mathematics,  where  familiarity 
with  truth  eliminates  the  vulgar  prejudices  of  common 
sense,  to  invest  Zeno's  paradoxes  with  the  respectable 
air  of  platitudes  ;  and  if  the  result  is  less  delightful  to  the 
lover  of  reason  than  Zeno's  bold  defiance,  it  is  at  any 
rate  more  calculated  to  appease  the  mass  of  academic 
mankind. 

Zeno  was  concerned,  as  a  matter  of  fact,  with  three 
problems,  each  presented  by  motion,  but  each  more 
abstract  than  motion,  and  capable  of  a  purely  arith- 
metical treatment.  These  are  the  problems  of  the 
infinitesimal,  the  infinite,  and  continuity.  To  state 
clearly  the  difficulties  involved,  was  to  accomplish  perhaps 
the  hardest  part  of  the  philosopher's  task.  This  was  done 
by  Zeno.  From  him  to  our  own  day,  the  finest  intellects 
of  each  generation  in  turn  attacked  the  problems,  but 
achieved,  broadly  speaking,  nothing.  In  our  own  time, 
however,  three  men — Weierstrass,  Dedekind,  and  Cantor 
— have  not  merely  advanced  the  three  problems,  but  have 
completely  solved  them.  The  solutions,  for  those  ac- 
quainted with  mathematics,  are  so  clear  as  to  leave  no 
longer  the  slightest  doubt  or  difficulty.  This  achieve- 
ment is  probably  the  greatest  of  which  our  age  has  to 
boast ;  and  I  know  of  no  age  (except  perhaps  the  golden 
G 


82  MYSTICISM   AND   LOGIC 

age  of  Greece)  which  has  a  more  convincing  proof  to  offer 
of  the  transcendent  genius  of  its  great  men.  Of  the  three 
problems,  that  of  the  infinitesimal  was  solved  by  Weier- 
strass  ;  the  solution  of  the  other  two  was  begun  by 
Dedekind,  and  definitively  accomplished  by  Cantor. 

The  infinitesimal  played  formerly  a  great  part  in 
mathematics.  It  was  introduced  by  the  Greeks,  who 
regarded  a  circle  as  differing  infinitesimally  from  a  polygon 
with  a  very  large  number  of  very  small  equal  sides.  It 
gradually  grew  in  importance,  until,  when  Leibniz  in- 
vented the  Infinitesimal  Calculus,  it  seemed  to  become 
the  fundamental  notion  of  all  higher  mathematics. 
Carlyle  tells,  in  his  Frederick  the  Great,  how  Leibniz  used 
to  discourse  to  Queen  Sophia  Charlotte  of  Prussia  con- 
cerning the  infinitely  little,  and  how  she  would  reply  that 
on  that  subject  she  needed  no  instruction — the  behaviour 
of  courtiers  had  made  her  thoroughly  familiar  with  it. 
But  philosophers  and  mathematicians — who  for  the  most 
part  had  less  acquaintance  with  courts — continued  to 
discuss  this  topic,  though  without  making  any  advance. 
The  Calculus  required  continuity,  and  continuity  was 
supposed  to  require  the  infinitely  little  ;  but  nobody 
could  discover  what  the  infinitely  little  might  be.  It  was 
plainly  not  quite  zero,  because  a  sufficiently  large  number 
of  infinitesimals,  added  together,  were  seen  to  make  up  a 
finite  whole.  But  nobody  could  point  out  any  fraction 
which  was  not  zero,  and  yet  not  finite.  Thus  there  was  a 
deadlock.  But  at  last  Weierstrass  discovered  that  the 
infinitesimal  was  not  needed  at  all,  and  that  everything 
could  be  accomplished  without  it.  Thus  there  was  no 
longer  any  need  to  suppose  that  there  was  such  a  thing. 
Nowadays,  therefore,  mathematicians  are  more  dignified 
than  Leibniz  :  instead  of  talking  about  the  infinitely 
small,  they  talk  about  the  infinitely  great — a  subject 


MATHEMATICS  AND  METAPHYSICIANS    83 

which,  however  appropriate  to  monarchs,  seems,  un- 
fortunately, to  interest  them  even  less  than  the  infinitely 
little  interested  the  monarchs  to  whom  Leibniz  discoursed. 

The  banishment  of  the  infinitesimal  has  all  sorts  of  odd 
consequences,  to  which  one  has  to  become  gradually 
accustomed.  For  example,  there  is  no  such  thing  as  the 
next  moment.  The  interval  between  one  moment  and  the 
next  would  have  to  be  infinitesimal,  since,  if  we  take  two 
moments  with  a  finite  interval  between  them,  there  are 
always  other  moments  in  the  interval.  Thus  if  there  are 
to  be  no  infinitesimals,  no  two  moments  are  quite  con- 
secutive, but  there  are  always  other  moments  between  any 
two.  Hence  there  must  be  an  infinite  number  of  moments 
between  any  two  ;  because  if  there  were  a  finite  number 
one  would  be  nearest  the  first  of  the  two  moments,  and 
therefore  next  to  it.  This  might  be  thought  to  be  a  diffi- 
culty ;  but,  as  a  matter  of  fact,  it  is  here  that  the  philo- 
sophy of  the  infinite  comes  in,  and  makes  all  straight. 

The  same  sort  of  thing  happens  in  space.  If  any  piece 
of  matter  be  cut  in  two,  and  then  each  part  be  halved, 
and  so  on,  the  bits  will  become  smaller  and  smaller,  and 
can  theoretically  be  made  as  small  as  we  please.  However 
small  they  may  be,  they  can  still  be  cut  up  and  made 
smaller  still.  But  they  will  always  have  some  finite  size, 
however  small  they  may  be.  We  never  reach  the  in- 
finitesimal in  this  way,  and  no  finite  number  of  divisions 
will  bring  us  to  points.  Nevertheless  there  are  points, 
only  these  are  not  to  be  reached  by  successive  divisions. 
Here  again,  the  philosophy  of  the  infinite  shows  us  how 
this  is  possible,  and  why  points  are  not  infinitesimal 
lengths. 

As  regards  motion  and  change,  we  get  similarly  curious 
results.  People  used  to  think  that  when  a  thing  changes, 
it  must  be  in  a  state  of  change,  and  that  when  a  thing 


84  MYSTICISM   AND   LOGIC 

moves,  it  is  in  a  state  of  motion.  This  is  now  known  to 
be  a  mistake.  When  a  body  moves,  all  that  can  be  said 
is  that  it  is  in  one  place  at  one  time  and  in  another  at 
another.  We  must  not  say  that  it  will  be  in  a  neighbour- 
ing place  at  the  next  instant,  since  there  is  no  next 
instant.  Philosophers  often  tell  us  that  when  a  body  is 
in  motion,  it  changes  its  position  within  the  instant.  To 
this  view  Zeno  long  ago  made  the  fatal  retort  that  every 
body  always  is  where  it  is  ;  but  a  retort  so  simple  and 
brief  was  not  of  the  kind  to  which  philosophers  are  accus- 
tomed to  give  weight,  and  they  have  continued  down  to 
our  own  day  to  repeat  the  same  phrases  which  roused  the 
Eleatic's  destructive  ardour.  It  was  only  recently  that 
it  became  possible  to  explain  motion  in  detail  in  accord- 
ance with  Zeno's  platitude,  and  in  opposition  to  the 
philosopher's  paradox.  We  may  now  at  last  indulge  the 
comfortable  belief  that  a  body  in  motion  is  just  as  truly 
where  it  is  as  a  body  at  rest.  Motion  consists  merely  in 
the  fact  that  bodies  are  sometimes  in  one  place  and  some- 
times in  another,  and  that  they  are  at  intermediate  places 
at  intermediate  times.  Only  those  who  have  waded 
through  the  quagmire  of  philosophic  speculation  on  this 
subject  can  realise  what  a  liberation  from  antique  pre- 
judices is  involved  in  this  simple  and  straightforward 
commonplace. 

The  philosophy  of  the  infinitesimal,  as  we  have  just 
seen,  is  mainly  negative.  People  used  to  believe  in  it, 
and  now  they  have  found  out  their  mistake.  The  philo^ 
sophy  of  the  infinite,  on  the  other  hand,  is  wholly  positive. 
It  was  formerly  supposed  that  infinite  numbers,  and  the 
mathematical  infinite  generally,  were  self-contradictory. 
But  as  it  was  obvious  that  there  were  infinities — for 
example,  the  number  of  numbers — the  contradictions  of 
infinity  seemed  unavoidable,  and  philosophy  seemed  to 


MATHEMATICS  AND  METAPHYSICIANS     85 

have  wandered  into  a  "  cul-de-sac."  This  difficulty  led 
to  Kant's  antinomies,  and  hence,  more  or  less  indirectly, 
to  much  of  Hegel's  dialectic  method.  Almost  all  current 
philosophy  is  upset  by  the  fact  (of  which  very  few  philo- 
sophers are  as  yet  aware)  that  all  the  ancient  and  respect- 
able contradictions  in  the  notion  of  the  infinite  have  been 
once  for  all  disposed  of.  The  method  by  which  this  has 
been  done  is  most  interesting  and  instructive.  In  the 
first  place,  though  people  had  talked  glibly  about  infinity 
ever  since  the  beginnings  of  Greek  thought,  nobody  had 
ever  thought  of  asking,  What  is  infinity  ?  If  any 
philosopher  had  been  asked  for  a  definition  of  infinity,  he 
might  have  produced  some  unintelligible  rigmarole,  but  he 
would  certainly  not  have  been  able  to  give  a  definition 
that  had  any  meaning  at  all.  Twenty  years  ago,  roughly 
speaking,  Dedekind  and  Cantor  asked  this  question,  and, 
what  is  more  remarkable,  they  answered  it.  They  found, 
that  is  to  say,  a  perfectly  precise  definition  of  an  infinite 
number  or  an  infinite  collection  of  things.  This  was  the 
first  and  perhaps  the  greatest  step.  It  then  remained  to 
examine  the  supposed  contradictions  in  this  notion. 
Here  Cantor  proceeded  in  the  only  proper  way.  He  took 
pairs  of  contradictory  propositions,  in  which  both  sides 
of  the  contradiction  would  be  usually  regarded  as  demon- 
strable, and  he  strictly  examined  the  supposed  proofs.  He 
found  that  all  proofs  adverse  to  infinity  involved  a  certain 
principle,  at  first  sight  obviously  true,  but  destructive, 
in  its  consequences,  of  almost  all  mathematics.  The 
proofs  favourable  to  infinity,  on  the  other  hand,  involved 
no  principle  that  had  evil  consequences.  It  thus  appeared 
that  common  sense  had  allowed  itself  to  be  taken  in  by  a 
specious  maxim,  and  that,  when  once  this  maxim  was 
rejected,  all  went  well. 
The  maxim  in  question  is,  that  if  one  collection  is  part 


86  MYSTICISM   AND   LOGIC 

of  another,  the  one  which  is  a  part  has  fewer  terms  than 
the  one  of  which  it  is  a  part.  This  maxim  is  true  of  finite 
numbers.  For  example,  Englishmen  are  only  some  among 
Europeans,  and  there  are  fewer  Englishmen  than  Euro- 
peans. But  when  we  come  to  infinite  numbers,  this  is  no 
longer  true.  This  breakdown  of  the  maxim  gives  us  the 
precise  definition  of  infinity.  A  collection  of  terms  is 
infinite  when  it  contains  as  parts  other  collections  which 
have  just  as  many  terms  as  it  has.  If  you  can  take  away 
some  of  the  terms  of  a  collection,  without  diminishing 
the  number  of  terms,  then  there  are  an  infinite  number 
of  terms  in  the  collection.  For  example,  there  are  just 
as  many  even  numbers  as  there  are  numbers  altogether, 
since  every  number  can  be  doubled.  This  may  be  seen 
by  putting  odd  and  even  numbers  together  in  one  row, 
and  even  numbers  alone  in  a  row  below  : — 

1,  2,  3,  4,  5,  ad  infinitum. 

2,  4,  6,  8,  10,  ad  infinitum. 

There  are  obviously  just  as  many  numbers  in  the  row 
below  as  in  the  row  above,  because  there  is  one  below  for 
each  one  above.  This  property,  which  was  formerly 
thought  to  be  a  contradiction,  is  now  transformed  into  a 
harmless  definition  of  infinity,  and  shows,  in  the  above 
case,  that  the  number  of  finite  numbers  is  infinite. 

But  the  uninitiated  may  wonder  how  it  is  possible  to 
deal  with  a  number  which  cannot  be  counted.  It  is  im- 
possible to  count  up  all  the  numbers,  one  by  one,  because, 
however  many  we  may  count,  there  are  always  more  to 
follow.  The  fact  is  that  counting  is  a  very  vulgar  and 
elementary  way  of  finding  out  how  many  terms  there 
are  in  a  collection.  And  in  any  case,  counting  gives  us 
what  mathematicians  call  the  ordinal  number  of  our 
terms  ;  that  is  to  say,  it  arranges  our  terms  in  an  order  or 


MATHEMATICS  AND  METAPHYSICIANS    87 

series,  and  its  result  tells  us  what  type  of  series  results 
from  this  arrangement.  In  other  words,  it  is  impossible 
to  count  things  without  counting  some  first  and  others 
afterwards,  so  that  counting  always  has  to  do  with  order. 
Now  when  there  are  only  a  finite  number  of  terms,  we 
can  count  them  in  any  order  we  like  ;  but  when  there  are 
an  infinite  number,  what  corresponds  to  counting  will 
give  us  quite  different  results  according  to  the  way  in 
which  we  carry  out  the  operation.  Thus  the  ordinal 
number,  which  results  from  what,  in  a  general  sense, 
may  be  called  counting,  depends  not  only  upon  how  many 
terms  we  have,  but  also  (where  the  number  of  terms  is 
infinite)  upon  the  way  in  which  the  terms  are  arranged. 

The  fundamental  infinite  numbers  are  not  ordinal,  but 
are  what  is  called  cardinal.  They  are  not  obtained  by 
putting  our  terms  in  order  and  counting  them,  but  by  a 
different  method,  which  tells  us,  to  begin  with,  whether  two 
collections  have  the  same  number  of  terms,  or,  if  not, 
which  is  the  greater.1  It  does  not  tell  us,  in  the  way  in 
which  counting  does,  what  number  of  terms  a  collection 
has  ;  but  if  we  define  a  number  as  the  number  of  terms 
in  such  and  such  a  collection,  then  this  method  enables 
us  to  discover  whether  some  other  collection  that  may  be 
mentioned  has  more  or  fewer  terms.  An  illustration  will 
show  how  this  is  done.  If  there  existed  some  country  in 
which,  for  one  reason  or  another,  it  was  impossible  to 
take  a  census,  but  in  which  it  was  known  that  every  man 
had  a  wife  and  every  woman  a  husband,  then  (provided 
polygamy  was  not  a  national  institution)  we  should  know, 
without  counting,  that  there  were  exactly  as  many  men 
as  there  were  women  in  that  country,  neither  more  nor 

1  [Note  added  in  1917.]  Although  some  infinite  numbers  are 
greater  than  some  others,  it  cannot  be  proved  that  of  any  two  infinite 
numbers  one  must  be  the  greater. 


88  MYSTICISM   AND   LOGIC 

less.  This  method  can  be  applied  generally.  If  there  is 
some  relation  which,  like  marriage,  connects  the  things 
in  one  collection  each  with  one  of  the  things  in  another 
collection,  and  vice  versa,  then  the  two  collections  have 
the  same  number  of  terms.  This  was  the  way  in  which 
we  found  that  there  are  as  many  even  numbers  as  there 
are  numbers.  Every  number  can  be  doubled,  and  every 
even  number  can  be  halved,  and  each  process  gives  just 
one  number  corresponding  to  the  one  that  is  doubled  or 
halved.  And  in  this  way  we  can  find  any  number  of 
collections  each  of  which  has  just  as  many  terms  as  there 
are  finite  numbers.  If  every  term  of  a  collection  can  be 
hooked  on  to  a  number,  and  all  the  finite  numbers  are 
used  once,  and  only  once,  in  the  process,  then  our 
collection  must  have  just  as  many  terms  as  there  are 
finite  numbers.  This  is  the  general  method  by  which  the 
numbers  of  infinite  collections  are  defined. 

But  it  must  not  be  supposed  that  all  infinite  numbers 
are  equal.  On  the  contrary,  there  are  infinitely  more 
infinite  numbers  than  finite  ones.  There  are  more  ways 
of  arranging  the  finite  numbers  in  different  types  of 
series  than  there  are  finite  numbers.  There  are  probably 
more  points  in  space  and  more  moments  in  time  than 
there  are  finite  numbers.  There  are  exactly  as  many 
fractions  as  whole  numbers,  although  there  are  an  infinite 
number  of  fractions  between  any  two  whole  numbers. 
But  there  are  more  irrational  numbers  than  there  are 
whole  numbers  or  fractions.  There  are  probably  exactly 
as  many  points  in  space  as  there  are  irrational  numbers, 
and  exactly  as  many  points  on  a  line  a  millionth  of  an 
inch  long  as  in  the  whole  of  infinite  space.  There  is  a 
greatest  of  all  infinite  numbers,  which  is  the  number  of 
things  altogether,  of  every  sort  and  kind.  It  is  obvious 
that  there  cannot  be  a  greater  number  than  this,  because, 


MATHEMATICS  AND  METAPHYSICIANS    89 

if  everything  has  been  taken,  there  is  nothing  left  to  add. 
Cantor  has  a  proof  that  there  is  no  greatest  number,  and 
if  this  proof  were  valid,  the  contradictions  of  infinity 
would  reappear  in  a  sublimated  form.  But  in  this  one 
point,  the  master  has  been  guilty  of  a  very  subtle  fallacy, 
which  I  hope  to  explain  in  some  future  work.1 

We  can  now  understand  why  Zeno  believed  that  Achilles 
cannot  overtake  the  tortoise  and  why  as  a  matter  of  fact 
he  can  overtake  it.  We  shall  see  that  all  the  people  who 
disagreed  with  Zeno  had  no  right  to  do  so,  because  they 
all  accepted  premises  from  which  his  conclusion  followed. 
The  argument  is  this  :  Let  Achilles  and  the  tortoise  start 
along  a  road  at  the  same  time,  the  tortoise  (as  is  only 
fair)  being  allowed  a  handicap.  Let  Achilles  go  twice  as 
fast  as  the  tortoise,  or  ten  times  or  a  hundred  tunes  as 
fast.  Then  he  will  never  reach  the  tortoise.  For  at  every 
moment  the  tortoise  is  somewhere  and  Achilles  is  some- 
where ;  and  neither  is  ever  twice  in  the  same  place  while 
the  race  is  going  on.  Thus  the  tortoise  goes  to  just  as 
many  places  as  Achilles  does,  because  each  is  in  one  place 
at  one  moment,  and  in  another  at  any  other  moment. 
But  if  Achilles  were  to  catch  up  with  the  tortoise,  the 
places  where  the  tortoise  would  have  been  would  be  only 
part  of  the  places  where  Achilles  would  have  been.  Here, 
we  must  suppose,  Zeno  appealed  to  the  maxim  that  the 
whole  has  more  terms  that  the  part.2  Thus  if  Achilles  were 

1  Cantor  was  not  guilty  of  a  fallacy  on  this  point.     His  proof 
that  there  is  no  greatest  number  is  valid.     The  solution  of  the  puzzle 
is  complicated  and  depends  upon  the  theory  of  types,  which  is  explained 
in  Principia  Mathematica,  Vol.  I  (Camb.  Univ.  Press,  1910).     [Note 
added  in  1917.] 

2  This  must  not  be  regarded  as  a  historically  correct  account  of 
what  Zeno  actually  had  in  mind.     It  is  a  new  argument  for  his  con- 
clusion, not  the  argument  which  influenced  him.      On  this  point,  see 
e.g.  C.  D.  Broad,  "Note  on  Achilles  and  the  Tortoise,"  Mind,  N.S., 
Vol.  XXII,  pp.  318-19.     Much  valuable  work  on  the  interpretation  of 
Zeno  has  been  done  since  this  article  was  written.    [Note  added  in  191 7.] 


go  MYSTICISM   AND   LOGIC 

to  overtake  the  tortoise,  he  would  have  been  in  more 
places  than  the  tortoise  ;  but  we  saw  that  he  must,  in  any 
period,  be  in  exactly  as  many  places  as  the  tortoise. 
Hence  we  infer  that  he  can  never  catch  the  tortoise.  This 
argument  is  strictly  correct,  if  we  allow  the  axiom  that 
the  whole  has  more  terms  than  the  part.  As  the  con- 
clusion is  absurd,  the  axiom  must  be  rejected,  and  then 
all  goes  well.  But  there  is  no  good  word  to  be  said  for 
the  philosophers  of  the  past  two  thousand  years  and 
more,  who  have  all  allowed  the  axiom  and  denied  the 
conclusion. 

The  retention  of  this  axiom  leads  to  absolute  contra- 
dictions, while  its  rejection  leads  only  to  oddities.  Some 
of  these  oddities,  it  must  be  confessed,  are  very  odd. 
One  of  them,  which  I  call  the  paradox  of  Tristram  Shandy, 
is  the  converse  of  the  Achilles,  and  shows  that  the  tortoise, 
if  you  give  him  time,  will  go  just  as  far  as  Achilles. 
Tristram  Shandy,  as  we  know,  employed  two  years  in 
chronicling  the  first  two  days  of  his  life,  and  lamented 
that,  at  this  rate,  material  would  accumulate  faster  than 
he  could  deal  with  it,  so  that,  as  years  went  by,  he  would 
be  farther  and  farther  from  the  end  of  his  history.  Now 
I  maintain  that,  if  he  had  lived  for  ever,  and  had  not 
wearied  of  his  task,  then,  even  if  his  life  had  continued 
as  eventfully  as  it  began,  no  part  of  his  biography  would 
have  remained  unwritten.  For  consider  :  the  hundredth 
day  will  be  described  in  the  hundredth  year,  the  thousandth 
in  the  thousandth  year,  and  so  on.  Whatever  day  we 
may  choose  as  so  far  on  that  he  cannot  hope  to  reach  it, 
that  day  will  be  described  in  the  corresponding  year. 
Thus  any  day  that  may  be  mentioned  will  be  written  up 
sooner  or  later,  and  therefore  no  part  of  the  biography 
will  remain  permanently  unwritten.  This  paradoxical 
but  perfectly  true  proposition  depends  upon  the  fact 


MATHEMATICS  AND  METAPHYSICIANS    91 

that  the  number  of  days  in  all  time  is  no  greater  than  the 
number  of  years. 

Thus  on  the  subject  of  infinity  it  is  impossible  to  avoid 
conclusions  which  at  first  sight  appear  paradoxical,  and 
this  is  the  reason  why  so  many  philosophers  have  supposed 
that  there  were  inherent  contradictions  in  the  infinite. 
But  a  little  practice  enables  one  to  grasp  the  true  prin- 
ciples of  Cantor's  doctrine,  and  to  acquire  new  and 
better  instincts  as  to  the  true  and  the  false.  The  oddities 
then  become  no  odder  than  the  people  at  the  antipodes, 
who  used  to  be  thought  impossible  because  they  would 
find  it  so  inconvenient  to  stand  on  their  heads. 

The  solution  of  the  problems  concerning  infinity  has 
enabled  Cantor  to  solve  also  the  problems  of  continuity. 
Of  this,  as  of  infinity,  he  has  given  a  perfectly  precise 
definition,  and  has  shown  that  there  are  no  contradictions 
in  the  notion  so  defined.  But  this  subject  is  so  technical 
that  it  is  impossible  to  give  any  account  of  it  here. 

The  notion  of  continuity  depends  upon  that  of  order, 
since  continuity  is  merely  a  particular  type  of  order. 
Mathematics  has,  in  modern  times,  brought  order  into 
greater  and  greater  prominence.  In  former  days,  it  was 
supposed  (and  philosophers  are  still  apt  to  suppose)  that 
quantity  was  the  fundamental  notion  of  mathematics. 
But  nowadays,  quantity  is  banished  altogether,  except 
from  one  little  corner  of  Geometry,  while  order  more  and 
more  reigns  supreme.  The  investigation  of  different 
kinds  of  series  and  their  relations  is  now  a  very  large  part 
of  mathematics,  and  it  has  been  found  that  this  investiga- 
tion can  be  conducted  without  any  reference  to  quantity, 
and,  for  the  most  part,  without  any  reference  to  number. 
All  types  of  series  are  capable  of  formal  definition,  and 
their  properties  can  be  deduced  from  the  principles  of 
symbolic  logic  by  means  of  the  Algebra  of  Relatives. 


92  MYSTICISM   AND   LOGIC 

The  notion  of  a  limit,  which  is  fundamental  in  the  greater 
part  of  higher  mathematics,  used  to  be  denned  by  means 
of  quantity,  as  a  term  to  which  the  terms  of  some  series 
approximate  as  nearly  as  we  please.  But  nowadays  the 
limit  is  defined  quite  differently,  and  the  series  which  it 
limits  may  not  approximate  to  it  at  all.  This  improve- 
ment also  is  due  to  Cantor,  and  it  is  one  which  has 
revolutionised  mathematics.  Only  order  is  now  relevant 
to  limits.  Thus,  for  instance,  the  smallest  of  the  infinite 
integers  is  the  limit  of  the  finite  integers,  though  all 
finite  integers  are  at  an  infinite  distance  from  it.  The 
study  of  different  types  of  series  is  a  general  subject  of 
which  the  study  of  ordinal  numbers  (mentioned  above)  is 
a  special  and  very  interesting  branch.  But  the  unavoid- 
able technicalities  of  this  subject  render  it  impossible  to 
explain  to  any  but  professed  mathematicians. 

Geometry,  like  Arithmetic,  has  been  subsumed,  in 
recent  times,  under  the  general  study  of  order.  It  was 
formerly  supposed  that  Geometry  was  the  study  of  the 
nature  of  the  space  in  which  we  live,  and  accordingly  it 
was  urged,  by  those  who  held  that  what  exists  can  only 
be  known  empirically,  that  Geometry  should  really  be 
regarded  as  belonging  to  applied  mathematics.  But  it 
has  gradually  appeared,  by  the  increase  of  non-Euclidean 
systems,  that  Geometry  throws  no  more  light  upon  the 
nature  of  space  than  Arithmetic  throws  upon  the  popula- 
tion of  the  United  States.  Geometry  is  a  whole  collection 
of  deductive  sciences  based  on  a  corresponding  collection 
of  sets  of  axioms.  One  set  of  axioms  is  Euclid's  ;  other 
equally  good  sets  of  axioms  lead  to  other  results.  Whether 
Euclid's  axioms  are  true,  is  a  question  as  to  which  the 
the  pure  mathematician  is  indifferent ;  and,  what  is  more, 
it  is  a  question  which  it  is  theoretically  impossible  to 
answer  with  certainty  in  the  affirmative.  It  might  pos- 


MATHEMATICS  AND  METAPHYSICIANS    93 

sibly  be  shown,  by  very  careful  measurements,  that 
Euclid's  axioms  are  false ;  but  no  measurements  could 
ever  assure  us  (owing  to  the  errors  of  observation)  that 
they  are  exactly  true.  Thus  the  geometer  leaves  to  the 
man  of  science  to  decide,  as  best  he  may,  what  axioms  are 
most  nearly  true  in  the  actual  world.  The  geometer 
takes  any  set  of  axioms  that  seem  interesting,  and 
deduces  their  consequences.  What  defines  Geometry, 
in  this  sense,  is  that  the  axioms  must  give  rise  to  a  series 
of  more  than  one  dimension .  And  it  is  thus  that  Geometry 
becomes  a  department  in  the  study  of  order. 

In  Geometry,  as  in  other  parts  of  mathematics,  Peano 
and  his  disciples  have  done  work  of  the  very  greatest 
merit  as  regards  principles.  Formerly,  it  was  held  by 
philosophers  and  mathematicians  alike  that  the  proofs  in 
Geometry  depended  on  the  figure  ;  nowadays,  this  is 
known  to  be  false.  In  the  best  books  there  are  no  figures 
at  all.  The  reasoning  proceeds  by  the  strict  rules  of 
formal  logic  from  a  set  of  axioms  laid  down  to  begin  with. 
If  a  figure  is  used,  all  sorts  of  things  seem  obviously  to 
follow,  which  no  formal  reasoning  can  prove  from  the 
explicit  axioms,  and  which,  as  a  matter  of  fact,  are  only 
accepted  because  they  are  obvious.  By  banishing  the 
figure,  it  becomes  possible  to  discover  all  the  axioms  that 
are  needed  ;  and  in  this  way  all  sorts  of  possibilities, 
which  would  have  otherwise  remained  undetected,  are 
brought  to  light. 

One  great  advance,  from  the  point  of  view  of  correct- 
ness, has  been  made  by  introducing  points  as  they  are 
required,  and  not  starting,  as  was  formerly  done,  by 
assuming  the  whole  of  space.  This  method  is  due  partly 
to  Peano,  partly  to  another  Italian  named  Fano.  To 
those  unaccustomed  to  it,  it  has  an  air  of  somewhat 
wilful  pedantry.  In  this  way,  we  begin  with  the  following 


94  MYSTICISM   AND   LOGIC 

axioms  :  (i)  There  is  a  class  of  entities  called  points. 
(2)  There  is  at  least  one  point.  (3)  If  a  be  a  point,  there 
is  at  least  one  other  point  besides  a.  Then  we  bring  in 
the  straight  line  joining  two  points,  and  begin  again  with 
(4),  namely,  on  the  straight  line  joining  a  and  b,  there  is 
at  least  one  other  point  besides  a  and  b.  (5)  There  is  at 
least  one  point  not  on  the  line  ab.  And  so  we  go  on,  till 
we  have  the  means  of  obtaining  as  many  points  as  we 
require.  But  the  word  space,  as  Peano  humorously 
remarks,  is  one  for  which  Geometry  has  no  use  at  all. 

The  rigid  methods  employed  by  modern  geometers 
have  deposed  Euclid  from  his  pinnacle  of  correctness.  It 
was  thought,  until  recent  times,  that,  as  Sir  Henry  Savile 
remarked  in  1621,  there  were  only  two  blemishes  in 
Euclid,  the  theory  of  parallels  and  the  theory  of  pro- 
portion. It  is  now  known  that  these  are  almost  the  only 
points  in  which  Euclid  is  free  from  blemish.  Countless 
errors  are  involved  in  his  first  eight  propositions.  That 
is  to  say,  not  only  is  it  doubtful  whether  his  axioms  are 
true,  which  is  a  comparatively  trivial  matter,  but  it  is 
certain  that  his  propositions  do  not  follow  from  the 
axioms  which  he  enunciates.  A  vastly  greater  number 
of  axioms,  which  Euclid  unconsciously  employs,  are  re- 
quired for  the  proof  of  his  propositions.  Even  in  the 
first  proposition  of  all,  where  he  constructs  an  equilateral 
triangle  on  a  given  base,  he  uses  two  circles  which  are 
assumed  to  intersect.  But  no  explicit  axiom  assures  us 
that  they  do  so,  and  in  some  kinds  of  spaces  they  do  not 
always  intersect.  It  is  quite  doubtful  whether  our  space 
belongs  to  one  of  these  kinds  or  not.  Thus  Euclid  fails 
entirely  to  prove  his  point  in  the  very  first  proposition. 
As  he  is  certainly  not  an  easy  author,  and  is  terribly  long- 
winded,  he  has  no  longer  any  but  an  historical  interest. 
Under  these  circumstances,  it  is  nothing  less  than  a 


MATHEMATICS  AND  METAPHYSICIANS    95 

scandal  that  he  should  still  be  taught  to  boys  in  England.1 
A  book  should  have  either  intelligibility  or  correctness  ; 
to  combine  the  two  is  impossible,  but  to  lack  both  is  to 
be  unworthy  of  such  a  place  as  Euclid  has  occupied  in 
education. 

The  most  remarkable  result  of  modern  methods  in 
mathematics  is  the  importance  of  symbolic  logic  and  of 
rigid  formalism.  Mathematicians,  under  the  influence  of 
Weierstrass,  have  shown  in  modern  times  a  care  for 
accuracy,  and  an  aversion  to  slipshod  reasoning,  such  as 
had  not  been  known  among  them  previously  since  the  time 
of  the  Greeks.  The  great  inventions  of  the  seventeenth 
century — Analytical  Geometry  and  the  Infinitesimal 
Calculus — were  so  fruitful  in  new  results  that  mathe- 
maticians had  neither  time  nor  inclination  to  examine 
their  foundations.  Philosophers,  who  should  have  taken 
up  the  task,  had  too  little  mathematical  ability  to  invent 
the  new  branches  of  mathematics  which  have  now  been 
found  necessary  for  any  adequate  discussion.  Thus 
mathematicians  were  only  awakened  from  their  "  dog- 
matic slumbers "  when  Weierstrass  and  his  followers 
showed  that  many  of  their  most  cherished  propositions 
are  in  general  false.  Macaulay,  contrasting  the  certainty 
of  mathematics  with  the  uncertainty  of  philosophy,  asks 
who  ever  heard  of  a  reaction  against  Taylor's  theorem  ? 
If  he  had  lived  now,  he  himself  might  have  heard  of  such 
a  reaction,  for  this  is  precisely  one  of  the  theorems  which 
modern  investigations  have  overthrown.  Such  rude 
shocks  to  mathematical  faith  have  produced  that  love  of 
formalism  which  appears,  to  those  who  are  ignorant  of 
its  motive,  to  be  mere  outrageous  pedantry. 

1  Since  the  above  was  written,  he  has  ceased  to  be  used  as  a  text- 
book. But  I  fear  many  of  the  books  now  used  are  so  bad  that  the 
change  is  no  great  improvement.  [Note  added  in  1917.] 


96  MYSTICISM   AND   LOGIC 

The  proof  that  all  pure  mathematics,  including 
Geometry,  is  nothing  but  formal  logic,  is  a  fatal  blow  to 
the  Kantian  philosophy.  Kant,  rightly  perceiving  that 
Euclid's  propositions  could  not  be  deduced  from  Euclid's 
axioms  without  the  help  of  the  figures,  invented  a  theory 
of  knowledge  to  account  for  this  fact ;  and  it  accounted 
so  successfully  that,  when  the  fact  is  shown  to  be  a  mere 
defect  in  Euclid,  and  not  a  result  of  the  nature  of  geo- 
metrical reasoning,  Kant's  theory  also  has  to  be  aban- 
doned. The  whole  doctrine  of  a  priori  intuitions,  by  which 
Kant  explained  the  possibility  of  pure  mathematics,  is 
wholly  inapplicable  to  mathematics  in  its  present  form. 
The  Aristotelian  doctrines  of  the  schoolmen  come  nearer 
in  spirit  to  the  doctrines  which  modern  mathematics 
inspire  ;  but  the  schoolmen  were  hampered  by  the  fact 
that  their  formal  logic  was  very  defective,  and  that  the 
philosophical  logic  based  upon  the  syllogism  showed  a 
corresponding  narrowness.  What  is  now  required  is  to 
give  the  greatest  possible  development  to  mathematical 
logic,  to  allow  to  the  full  the  importance  of  relations,  and 
then  to  found  upon  this  secure  basis  a  new  philosophical 
logic,  which  may  hope  to  borrow  some  of  the  exactitude 
and  certainty  of  its  mathematical  foundation.  If  this 
can  be  successfully  accomplished,  there  is  every  reason 
to  hope  that  the  near  future  will  be  as  great  an  epoch  in 
pure  philosophy  as  the  immediate  past  has  been  in  the 
principles  of  mathematics.  Great  triumphs  inspire  great 
hopes ;  and  pure  thought  may  achieve,  within  our 
generation,  such  results  as  will  place  our  time,  in  this 
respect,  on  a  level  with  the  greatest  age  of  Greece.1 

1  The  greatest  age  of  Greece  was  brought  to  an  end  by  the 
Peloponnesian  War.  [Note  added  in  1917.] 


VI 

ON   SCIENTIFIC   METHOD   IN 
PHILOSOPHY 

WHEN  we  try  to  ascertain  the  motives  which  have 
led  men  to  the  investigation  of  philosophical 
questions,  we  find  that,  broadly  speaking,  they  can  be 
divided  into  two  groups,  often  antagonistic,  and  leading 
to  very  divergent  systems.  These  two  groups  of  motives 
are,  on  the  one  hand,  those  derived  from  religion  and 
ethics,  and,  on  the  other  hand,  those  derived  from  science. 
Plato,  Spinoza,  and  Hegel  may  be  taken  as  typical  of  the 
philosophers  whose  interests  are  mainly  religious  and 
ethical,  while  Leibniz,  Locke,  and  Hume  may  be  taken  as 
representatives  of  the  scientific  wing.  In  Aristotle, 
Descartes,  Berkeley,  and  Kant  we  find  both  groups  of 
motives  strongly  present. 

Herbert  Spencer,  in  whose  honour  we  are  assembled 
to-day,  would  naturally  be  classed  among  scientific 
philosophers  :  it  was  mainly  from  science  that  he  drew 
his  data,  his  formulation  of  problems,  and  his  conception 
of  method.  But  his  strong  religious  sense  is  obvious 
in  much  of  his  writing,  and  his  ethical  preoccupations 
are  what  make  him  value  the  conception  of  evolution — 
that  conception  in  which,  as  a  whole  generation  has 
believed,  science  and  morals  are  to  be  united  in  fruitful 
and  indissoluble  marriage. 

It  is  my  belief  that  the  ethical  and  religious  motives, 
H  97 


98 

in  spite  of  the  splendidly  imaginative  systems  to  which 
they  have  given  rise,  have  been  on  the  whole  a  hindrance 
to  the  progress  of  philosophy,  and  ought  now  to  be 
consciously  thrust  aside  by  those  who  wish  to  discover 
philosophical  truth.  Science,  originally,  was  entangled 
in  similar  motives,  and  was  thereby  hindered  in  its 
advances.  It  is,  I  maintain,  from  science,  rather  than 
from  ethics  and  religion,  that  philosophy  should  draw 
its  inspiration. 

But  there  are  two  different  ways  in  which  a  philosophy 
may  seek  to  base  itself  upon  science.  It  may  emphasise 
the  most  general  results  of  science,  and  seek  to  give  even 
greater  generality  and  unity  to  these  results.  Or  it  may 
study  the  methods  of  science,  and  seek  to  apply  these 
methods,  with  the  necessary  adaptations,  to  its  own 
peculiar  province.  Much  philosophy  inspired  by  science 
has  gone  astray  through  preoccupation  with  the  results 
momentarily  supposed  to  have  been  achieved.  It  is  not 
results,  but  methods,  that  can  be  transferred  with  profit 
from  the  sphere  of  the  special  sciences  to  the  sphere  of 
philosophy.  What  I  wish  to  bring  to  your  notice  is  the 
possibility  and  importance  of  applying  to  philosophical 
problems  certain  broad  principles  of  method  which  have 
been  found  successful  in  the  study  of  scientific  questions. 

The  opposition  between  a  philosophy  guided  by 
scientific  method  and  a  philosophy  dominated  by  religious 
and  ethical  ideas  may  be  illustrated  by  two  notions  which 
are  very  prevalent  in  the  works  of  philosophers,  namely 
the  notion  of  the  universe,  and  the  notion  of  good  and 
evil.  A  philosopher  is  expected  to  tell  us  something  about 
the  nature  of  the  universe  as  a  whole,  and  to  give  grounds 
for  either  optimism  or  pessimism.  Both  these  expecta- 
tions seem  to  me  mistaken.  I  believe  the  conception 
of  "the  universe  "  to  be,  as  its  etymology  indicates,  a 


SCIENTIFIC  METHOD  IN  PHILOSOPHY     99 

mere  relic  of  pre-Copernican  astronomy  :  and  I  believe 
the  question  of  optimism  and  pessimism  to  be  one  which 
the  philosopher  will  regard  as  outside  his  scope,  except, 
possibly,  to  the  extent  of  maintaining  that  it  is  insoluble. 

In  the  days  before  Copernicus,  the  conception  of  the 
"  universe  "  was  defensible  on  scientific  grounds  :  the 
diurnal  revolution  of  the  heavenly  bodies  bound  them 
together  as  all  parts  of  one  system,  of  which  the  earth 
was  the  centre.  Round  this  apparent  scientific  fact, 
many  human  desires  rallied  :  the  wish  to  believe  Man 
important  in  the  scheme  of  things,  the  theoretical  desire 
for  a  comprehensive  understanding  of  the  Whole,  the 
hope  that  the  course  of  nature  might  be  guided  by  some 
sympathy  with  our  wishes.  In  this  way,  an  ethically 
inspired  system  of  metaphysics  grew  up,  whose  anthro- 
pocentrism  was  apparently  warranted  by  the  geocentrism 
of  astronomy.  When  Copernicus  swept  away  the  astrono- 
mical basis  of  this  system  of  thought,  it  had  grown  so 
familiar,  and  had  associated  itself  so  intimately  with  men's 
aspirations,  that  it  survived  with  scarcely  diminished 
force — survived  even  Kant's  "  Copernican  revolution," 
and  is  still  now  the  unconscious  premiss  of  most  meta- 
physical systems. 

The  oneness  of  the  world  is  an  almost  undiscussed 
postulate  of  most  metaphysics.  "  Reality  is  not  merely 
one  and  self-consistent,  but  is  a  system  of  reciprocally 
determinate  parts"1 — such  a  statement  would  pass  almost 
unnoticed  as  a  mere  truism.  Yet  I  believe  that  it  em- 
bodies a  failure  to  effect  thoroughly  the  "  Copernican 
revolution,"  and  that  the  apparent  oneness  of  the  world 
is  merely  the  oneness  of  what  is  seen  by  a  single  spectator 
or  apprehended  by  a  single  mind.  The  Critical  Philosophy, 
although  it  intended  to  emphasise  the  subjective  element 

1  Bosanquet,  Logic,  ii,  p.  211. 


ioo  MYSTICISM   AND   LOGIC 

in  many  apparent  characteristics  of  the  world,  yet,  by 
regarding  the  world  in  itself  as  unknowable,  so  con- 
centrated attention  upon  the  subjective  representation 
that  its  subjectivity  was  soon  forgotten.  Having  re- 
cognised the  categories  as  the  work  of  the  mind,  it  was 
paralysed  by  its  own  recognition,  and  abandoned  in 
despair  the  attempt  to  undo  the  work  of  subjective 
falsification.  In  part,  no  doubt,  its  despair  was  well 
founded,  but  not,  I  think,  in  any  absolute  or  ultimate 
sense.  Still  less  was  it  a  ground  for  rejoicing,  or  for 
supposing  that  the  nescience  to  which  it  ought  to  have 
given  rise  could  be  legitimately  exchanged  for  a  meta- 
physical dogmatism. 


As  regards  our  present  question,  namely,  the  question 
of  the  unity  of  the  world,  the  right  method,  as  I  think, 
has  been  indicated  by  William  James.1  "  Let  us  now 
turn  our  backs  upon  ineffable  or  unintelligible  ways 
of  accounting  for  the  world's  oneness,  and  inquire  whether, 
instead  of  being  a  principle,  the  '  oneness  '  affirmed  may 
not  merely  be  a  name  like  '  substance'  descriptive  of 
the  fact  that  certain  specific  and  verifiable  connections 
are  found  among  the  parts  of  the  experiential  flux.  .  .  . 
We  can  easily  conceive  of  things  that  shall  have  no  connec- 
tion whatever  with  each  other.  We  may  assume  them 
to  inhabit  different  times  and  spaces,  as  the  dreams  of 
different  persons  do  even  now.  They  may  be  so  unlike 
and  incommensurable,  and  so  inert  towards  one  another, 
as  never  to  jostle  or  interfere.  Even  now  there  may 
actually  be  whole  universes  so  disparate  from  ours  that 
we  who  know  ours  have  no  means  of  perceiving  that  they 
exist.  We  conceive  their  diversity,  however  ;  and  by  that 

1  Some  Problems  of  Philosophy,  p.  124. 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    101 

fact  the  whole  lot  of  them  form  what  is  known  in  logic 
as  '  a  universe  of  discourse.'  To  form  a  universe  of 
discourse  argues,  as  this  example  shows,  no  further  kind 
of  connexion .  The  importance  attached  by  certain  monistic 
writers  to  the  fact  that  any  chaos  may  become  a  universe 
by  merely  being  named,  is  to  me  incomprehensible." 
We  are  thus  left  with  two  kinds  of  unity  in  the  experienced 
world  ;  the  one  what  we  may  call  the  epistemological 
unity,  due  merely  to  the  fact  that  my  experienced  world 
is  what  one  experience  selects  from  the  sum  total  of 
existence  ;  the  other  that  tentative  and  partial  unity 
exhibited  in  the  prevalence  of  scientific  laws  in  those 
portions  of  the  world  which  science  has  hitherto  mastered. 
Now  a  generalisation  based  upon  either  of  these  kinds  of 
unity  would  be  fallacious.  That  the  things  which  we 
experience  have  the  common  property  of  being  ex- 
perienced by  us  is  a  truism  from  which  obviously  nothing 
of  importance  can  be  deducible  :  it  is  clearly  fallacious 
to  draw  from  the  fact  that  whatever  we  experience  is 
experienced  the  conclusion  that  therefore  everything 
must  be  experienced.  The  generalisation  of  the  second 
kind  of  unity,  namely,  that  derived  from  scientific  laws, 
would  be  equally  fallacious,  though  the  fallacy  is  a  trifle 
less  elementary.  In  order  to  explain  it  let  us  consider 
for  a  moment  what  is  called  the  reign  of  law.  People 
often  speak  as  though  it  were  a  remarkable  fact  that  the 
physical  world  is  subject  to  invariable  laws.  In  fact, 
however,  it  is  not  easy  to  see  how  such  a  world  could 
fail  to  obey  general  laws.  Taking  any  arbitrary  set 
of  points  in  space,  there  is  a  function  of  the  time  corre- 
sponding to  these  points,  i.e.  expressing  the  motion  of  a 
particle  which  traverses  these  points  :  this  function  may 
be  regarded  as  a  general  law  to  which  the  behaviour  of 
such  a  particle  is  subject.  Taking  all  such  functions  for 


102  MYSTICISM   AND   LOGIC 

all  the  particles  in  the  universe,  there  will  be  theo- 
retically some  one  formula  embracing  them  all,  and  this 
formula  may  be  regarded  as  the  single  and  supreme  law 
of  the  spatio-temporal  world.  Thus  what  is  surprising 
in  physics  is  not  the  existence  of  general  laws,  but  their 
extreme  simplicity.  It  is  not  the  uniformity  of  nature 
that  should  surprise  us,  for,  by  sufficient  analytic  ingenuity, 
any  conceivable  course  of  nature  might  be  shown  to 
exhibit  uniformity.  What  should  surprise  us  is  the 
fact  that  the  uniformity  is  simple  enough  for  us  to  be 
able  to  discover  it.  But  it  is  just  this  characteristic 
of  simplicity  in  the  laws  of  nature  hitherto  discovered 
which  it  would  be  fallacious  to  generalise,  for  it  is  obvious 
that  simplicity  has  been  a  part  cause  of  their  discovery, 
and  can,  therefore,  give  no  ground  for  the  supposition 
that  other  undiscovered  laws  are  equally  simple. 

The  fallacies  to  which  these  two  kinds  of  unity  have 
given  rise  suggest  a  caution  as  regards  all  use  in  philoso- 
phy of  general  results  that  science  is  supposed  to  have 
achieved.  In  the  first  place,  in  generalising  these  results 
beyond  past  experience,  it  is  necessary  to  examine  very 
carefully  whether  there  is  not  some  reason  making  it 
more  probable  that  these  results  should  hold  of  all  that 
has  been  experienced  than  that  they  should  hold  of 
things  universally.  The  sum  total  of  what  is  experienced 
by  mankind  is  a  selection  from  the  sum  total  of  what 
exists,  and  any  general  character  exhibited  by  this 
selection  may  be  due  to  the  manner  of  selecting  rather 
than  to  the  general  character  of  that  from  which  ex- 
perience selects.  In  the  second  place,  the  most  general 
results  of  science  are  the  least  certain  and  the  most  liable  to 
be  upset  by  subsequent  research.  In  utilizing  these  results 
as  the  basis  of  a  philosophy,  we  sacrifice  the  most  valu- 
able and  remarkable  characteristic  of  scientific  method, 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    103 

namely,  that,  although  almost  everything  in  science  is 
found  sooner  or  later  to  require  some  correction,  yet  this 
correction  is  almost  always  such  as  to  leave  untouched,  or 
only  slightly  modified,  the  greater  part  of  the  results 
which  have  been  deduced  from  the  premiss  subsequently 
discovered  to  be  faulty.  The  prudent  man  of  science 
acquires  a  certain  instinct  as  to  the  kind  of  uses  which 
may  be  made  of  present  scientific  beliefs  without  incurring 
the  danger  of  complete  and  utter  refutation  from  the 
modifications  likely  to  be  introduced  by  subsequent 
discoveries .  Unfortunately  the  use  of  scientific  generalisa- 
tions of  a  sweeping  kind  as  the  basis  of  philosophy  is 
just  that  kind  of  use  which  an  instinct  of  scientific  caution 
would  avoid,  since,  as  a  rule,  it  would  only  lead  to  true 
results  if  the  generalisation  upon  which  it  is  based  stood 
in  no  need  of  correction. 

We  may  illustrate  these  general  considerations  by 
means  of  two  examples,  namely,  the  conservation  of 
energy  and  the  principle  of  evolution. 

(i)  Let  us  begin  with  the  conservation  of  energy,  or, 
as  Herbert  Spencer  used  to  call  it,  the  persistence  of 
force.  He  says  :J 

"  Before  taking  a  first  step  in  the  rational  inter- 
pretation of  Evolution,  it  is  needful  to  recognise, 
not  only  the  facts  that  Matter  is  indestructible  and 
Motion  continuous,  but  also  the  fact  that  Force 
persists.  An  attempt  to  assign  the  causes  of  Evo- 
lution would  manifestly  be  absurd  if  that  agency  to 
which  the  metamorphosis  in  general  and  in  detail 
is  due,  could  either  come  into  existence  or  cease  to 
exist.  The  succession  of  phenomena  would  in  such 
case  be  altogether  arbitrary,  and  deductive  Science 
impossible." 

1  First  Principles  (1862),  Part  II,  beginning  of  chap.  viii. 


104  MYSTICISM   AND   LOGIC 

This  paragraph  illustrates  the  kind  of  way  in  which 
the  philosopher  is  tempted  to  give  an  air  of  absoluteness 
and  necessity  to  empirical  generalisations,  of  which  only 
the  approximate  truth  in  the  regions  hitherto  investi- 
gated can  be  guaranteed  by  the  unaided  methods  of 
science.  It  is  very  often  said  that  the  persistence  of 
something  or  other  is  a  necessary  presupposition  of  all 
scientific  investigation,  and  this  presupposition  is  then 
thought  to  be  exemplified  in  some  quantity  which 
physics  declares  to  be  constant.  There  are  here,  as  it 
seems  to  me,  three  distinct  errors.  First,  the  detailed 
scientific  investigation  of  nature  does  not  presuppose  any 
such  general  laws  as  its  results  are  found  to  verify. 
Apart  from  particular  observations,  science  need  pre- 
suppose nothing  except  the  general  principles  of  logic, 
and  these  principles  are  not  laws  of  nature,  for  they  are 
merely  hypothetical,  and  apply  not  only  to  the  actual 
world  but  to  whatever  is  possible.  The  second  error 
consists  in  the  identification  of  a  constant  quantity  with 
a  persistent  entity.  Energy  is  a  certain  function  of 
a  physical  system,  but  is  not  a  thing  or  substance  per- 
sisting throughout  the  changes  of  the  system.  The  same 
is  true  of  mass,  in  spite  of  the  fact  that  mass  has  often 
been  defined  as  quantity  of  matter.  The  whole  conception, 
of  quantity,  involving,  as  it  does,  numerical  measurement 
based  largely  upon  conventions,  is  far  more  artificial, 
far  more  an  embodiment  of  mathematical  convenience, 
than  is  commonly  believed  by  those  who  philosophise 
on  physics.  Thus  even  if  (which  I  cannot  for  a  moment 
admit)  the  persistence  of  some  entity  were  among  the 
necessary  postulates  of  science,  it  would  be  a  sheer  error 
to  infer  from  this  the  constancy  of  any  physical  quantity, 
or  the  a  priori  necessity  of  any  such  constancy  which 
may  be  empirically  discovered.  In  the  third  place,  it 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    105 

has  become  more  and  more  evident  with  the  progress  of 
physics  that  large  generalisations,  such  as  the  conserva- 
tion of  energy  or  mass,  are  far  from  certain  and  are 
very  likely  only  approximate.  Mass,  which  used  to  be 
regarded  as  the  most  indubitable  of  physical  quantities, 
is  now  generally  believed  to  vary  according  to  velocity, 
and  to  be,  in  fact,  a  vector  quantity  which  at  a 
given  moment  is  different  in  different  directions.  The 
detailed  conclusions  deduced  from  the  supposed  constancy 
of  mass  for  such  motions  as  used  to  be  studied 
in  physics  will  remain  very  nearly  exact,  and  therefore 
over  the  field  of  the  older  investigations  very  little  modi- 
fication of  the  older  results  is  required.  But  as  soon  as 
such  a  principle  as  the  conservation  of  mass  or  of  energy 
is  erected  into  a  universal  a  priori  law,  the  slightest 
failure  in  absolute  exactness  is  fatal,  and  the  whole 
philosophic  structure  raised  upon  this  foundation  is 
necessarily  ruined.  The  prudent  philosopher,  there- 
fore, though  he  may  with  advantage  study  the 
methods  of  physics,  will  be  very  chary  of  basing 
anything  upon  what  happen  at  the  moment  to  be 
the  most  general  results  apparently  obtained  by  those 
methods. 

(2)  The  philosophy  of  evolution,  which  was  to  be  our 
second  example,  illustrates  the  same  tendency  to  hasty 
generalisation,  and  also  another  sort,  namely,  the  undue 
preoccupation  with  ethical  notions.  There  are  two 
kinds  of  evolutionist  philosophy,  of  which  both  Hegel 
and  Spencer  represent  the  older  and  less  radical  kind, 
while  Pragmatism  and  Bergson  represent  the  more 
modern  and  revolutionary  variety.  But  both  these  sorts 
of  evolutionism  have  in  common  the  emphasis  on  progress, 
that  is,  upon  a  continual  change  from  the  worse  to  the 
better,  or  from  the  simpler  to  the  more  complex.  It 


io6  MYSTICISM   AND   LOGIC 

would  be  unfair  to  attribute  to  Hegel  any  scientific 
motive  or  foundation,  but  all  the  other  evolutionists, 
including  Hegel's  modern  disciples,  have  derived  their 
impetus  very  largely  from  the  history  of  biological 
development.  To  a  philosophy  which  derives  a  law  of 
universal  progress  from  this  history  there  are  two  objec- 
tions. First,  that  this  history  itself  is  concerned  with  a 
very  small  selection  of  facts  confined  to  an  infinitesimal 
fragment  of  space  and  time,  and  even  on  scientific 
grounds  probably  not  an  average  sample  of  events 
in  the  world  at  large.  For  we  know  that  decay 
as  well  as  growth  is  a  normal  occurrence  in  the  world. 
An  extra-terrestrial  philosopher,  who  had  watched 
a  single  youth  up  to  the  age  of  twenty-one  and  had  never 
come  across  any  other  human  being,  might  conclude  that 
it  is  the  nature  of  human  beings  to  grow  continually 
taller  and  wiser  in  an  indefinite  progress  towards  per- 
fection ;  and  this  generalisation  would  be  just  as  well 
founded  as  the  generalisation  which  evolutionists  base 
upon  the  previous  history  of  this  planet.  Apart,  how- 
ever, from  this  scientific  objection  to  evolutionism, 
there  is  another,  derived  from  the  undue  admixture 
of  ethical  notions  in  the  very  idea  of  progress  from  which 
evolutionism  derives  its  charm.  Organic  life,  we  are  told, 
has  developed  gradually  from  the  protozoon  to  the 
philosopher,  and  this  development,  we  are  assured,  is 
indubitably  an  advance.  Unfortunately  it  is  the  philoso- 
pher, not  the  protozoon,  who  gives  us  this  assurance, 
and  we  can  have  no  security  that  the  impartial  outsider 
would  agree  with  the  philosopher's  self-complacent 
assumption.  This  point  has  been  illustrated  by  the 
philosopher  Chuang  Tzii  in  the  following  instructive 
anecdote  : 


"  The  Grand  Augur,  in  his  ceremonial  robes,  ap- 
proached the  shambles  and  thus  addressed  the  pigs  : 
'  How  can  you  object  to  die  ?  I  shall  fatten  you  for 
three  months.  I  shall  discipline  myself  for  ten  days 
and  fast  for  three.  I  shall  strew  fine  grass,  and  place 
you  bodily  upon  a  carved  sacrificial  dish.  Does  not 
this  satisfy  you  ?  ' 

Then,  speaking  from  the  pigs'  point  of  view,  he 
continued  :  '  It  is  better,  perhaps,  after  all,  to  live  on 
bran  and  escape  the  shambles.  .  .  .' 

'  But  then,'  added  he,  speaking  from  his  own  point 
of  view,  '  to  enjoy  honour  when  alive  one  would 
readily  die  on  a  war-shield  or  in  the  headsman's  basket.' 

So  he  rejected  the  pigs'  point  of  view  and  adopted 
his  own  point  of  view.  In  what  sense,  then,  was  he 
different  from  the  pigs  ?  " 

I  much  fear  that  the  evolutionists  too  often  resemble 
the  Grand  Augur  and  the  pigs. 

The  ethical  element  which  has  been  prominent  in 
many  of  the  most  famous  systems  of  philosophy  is,  in 
my  opinion,  one  of  the  most  serious  obstacles  to  the 
victory  of  scientific  method  in  the  investigation  of  philo- 
sophical questions.  Human  ethical  notions,  as  Chuang 
Tzu  perceived,  are  essentially  anthropocentric,  and 
involve,  when  used  in  metaphysics,  an  attempt,  how- 
ever veiled,  to  legislate  for  the  universe  on  the  basis  of  the 
present  desires  of  men.  In  this  way  they  interfere  with 
that  receptivity  to  fact  which  is  the  essence  of  the 
scientific  attitude  towards  the  world.  To  regard  ethical 
notions  as  a  key  to  the  understanding  of  the  world  is 
essentially  pre-Copernican.  It  is  to  make  man,  with  the 
hopes  and  ideals  which  he  happens  to  have  at  the  present 
moment,  the  centre  of  the  universe  and  the  interpreter  of 
its  supposed  aims  and  purposes.  Ethical  metaphysics 
is  fundamentally  an  attempt,  however  disguised,  to 


io8  MYSTICISM   AND   LOGIC 

give  legislative  force  to  our  own  wishes.  This  may,  of 
course,  be  questioned,  but  I  think  that  it  is  confirmed  by 
a  consideration  of  the  way  in  which  ethical  notions  arise. 
Ethics  is  essentially  a  product  of  the  gregarious  instinct, 
that  is  to  say,  of  the  instinct  to  co-operate  with  those 
who  are  to  form  our  own  group  against  those  who  belong 
to  other  groups.  Those  who  belong  to  our  own  group 
are  good  ;  those  who  belong  to  hostile  groups  are  wicked. 
The  ends  which  are  pursued  by  our  own  group  are  desir- 
able ends,  the  ends  pursued  by  hostile  groups  are  nefari- 
ous. The  subjectivity  of  this  situation  is  not  apparent 
to  the  gregarious  animal,  which  feels  that  the  general 
principles  of  justice  are  on  the  side  of  its  own  herd. 
When  the  animal  has  arrived  at  the  dignity  of  the  meta- 
physician, it  invents  ethics  as  the  embodiment  of  its 
belief  in  the  justice  of  its  own  herd.  So  the  Grand 
Augur  invokes  ethics  as  the  justification  of  Augurs  in 
their  conflicts  with  pigs.  But,  it  may  be  said,  this  view 
of  ethics  takes  no  account  of  such  truly  ethical  notions  as 
that  of  self-sacrifice.  This,  however,  would  be  a  mistake. 
The  success  of  gregarious  animals  in  the  struggle  for 
existence  depends  upon  co-operation  within  the  herd,  and 
co-operation  requires  sacrifice,  to  some  extent,  of  what 
would  otherwise  be  the  interest  of  the  individual.  Hence 
arises  a  conflict  of  desires  and  instincts,  since  both  self- 
preservation  and  the  preservation  of  the  herd  are  biological 
ends  to  the  individual.  Ethics  is  in  origin  the  art  of 
recommending  to  others  the  sacrifices  required  for  co-oper- 
ation with  oneself.  Hence,  by  reflexion,  it  comes,  through 
the  operation  of  social  justice,  to  recommend  sacrifices 
by  oneself,  but  all  ethics,  however  refined,  remains  more 
or  less  subjective.  Even  vegetarians  do  not  hesitate, 
for  example,  to  save  the  life  of  a  man  in  a  fever,  although 
in  doing  so  they  destroy  the  lives  of  many  millions  of 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    109 

microbes.  The  view  of  the  world  taken  by  the  philosophy 
derived  from  ethical  notions  is  thus  never  impartial 
and  therefore  never  fully  scientific.  As  compared  with 
science,  it  fails  to  achieve  the  imaginative  liberation  from 
self  which  is  necessary  to  such  understanding  of  the 
world  as  man  can  hope  to  achieve,  and  the  philosophy 
which  it  inspires  is  always  more  or  less  parochial, 
more  or  less  infected  with  the  prejudices  of  a  time  and 
a  place. 

I  do  not  deny  the  importance  or  value,  within  its  own 
sphere,  of  the  kind  of  philosophy  which  is  inspired  by 
ethical  notions.  The  ethical  work  of  Spinoza,  for  ex- 
ample, appears  to  me  of  the  very  highest  significance, 
but  what  is  valuable  in  such  work  is  not  any  meta- 
physical theory  as  to  the  nature  of  the  world  to  which 
it  may  give  rise,  nor  indeed  anything  which  can  be 
proved  or  disproved  by  argument.  What  is  valuable  is 
the  indication  of  some  new  way  of  feeling  towards  life 
and  the  world,  some  way  of  feeling  by  which  our  own 
existence  can  acquire  more  of  the  characteristics  which 
we  must  deeply  desire.  The  value  of  such  work,  how- 
ever immeasurable  it  is,  belongs  with  practice  and  not 
with  theory.  Such  theoretic  importance  as  it  may 
possess  is  only  in  relation  to  human  nature,  not  in  re- 
lation to  the  world  at  large.  The  scientific  philosophy, 
therefore,  which  aims  only  at  understanding  the  world 
and  not  directly  at  any  other  improvement  of  human 
life,  cannot  take  account  of  ethical  notions  without  being 
turned  aside  from  that  submission  to  fact  which  is  the 
essence  of  the  scientific  temper. 


no  MYSTICISM   AND   LOGIC 

ii 

If  the  notion  of  the  universe  and  the  notion  of  good 
and  evil  are  extruded  from  scientific  philosophy,  it  may 
be  asked  what  specific  problems  remain  for  the  philos- 
opher as  opposed  to  the  man  of  science  ?  It  would  be 
difficult  to  give  a  precise  answer  to  this  question,  but 
certain  characteristics  may  be  noted  as  distinguishing 
the  province  of  philosophy  from  that  of  the  special 
sciences. 

In  the  first  place  a  philosophical  proposition  must  be 
general.  It  must  not  deal  specially  with  things  on  the 
surface  of  the  earth,  or  with  the  solar  system,  or  with 
any  other  portion  of  space  and  time.  It  is  this  need  of 
generality  which  has  led  to  the  belief  that  philosophy 
deals  with  the  universe  as  a  whole.  I  do  not  believe 
that  this  belief  is  justified,  but  I  do  believe  that  a  philo- 
sophical proposition  must  be  applicable  to  everything 
that  exists  or  may  exist.  It  might  be  supposed  that  this 
admission  would  be  scarcely  distinguishable  from  the 
view  which  I  wish  to  reject.  This,  however,  would  be 
an  error,  and  an  important  one.  The  traditional  view 
would  make  the  universe  itself  the  subject  of  various 
predicates  which  could  not  be  applied  to  any  particular 
thing  in  the  universe,  and  the  ascription  of  such  peculiar 
predicates  to  the  universe  would  be  the  special  business 
of  philosophy.  I  maintain,  on  the  contrary,  that  there 
are  no  propositions  of  which  the  "  universe  "  is  the  sub- 
ject ;  in  other  words,  that  there  is  no  such  thing  as  the 
"  universe."  What  I  do  maintain  is  that  there  are 
general  propositions  which  may  be  asserted  of  each 
individual  thing,  such  as  the  propositions  of  logic.  This 
does  not  involve  that  all  the  things  there  are  form  a  whole 
which  could  be  regarded  as  another  thing  and  be  made 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    in 

the  subject  of  predicates.  It  involves  only  the  assertion 
that  there  are  properties  which  belong  to  each  separate 
thing,  not  that  there  are  properties  belonging  to  the 
whole  of  things  collectively.  The  philosophy  which 
I  wish  to  advocate  may  be  called  logical  atomism  or 
absolute  pluralism,  because,  while  maintaining  that 
there  are  many  things,  it  denies  that  there  is  a  whole 
composed  of  those  things.  We  shall  see,  therefore,  that 
philosophical  propositions,  instead  of  being  concerned 
with  the  whole  of  things  collectively,  are  concerned  with 
all  things  distributively  ;  and  not  only  must  they  be 
concerned  with  all  things,  but  they  must  be  concerned 
with  such  properties  of  all  things  as  do  not  depend  upon 
the  accidental  nature  of  the  things  that  there  happen  to 
be,  but  are  true  of  any  possible  world,  independently  of 
such  facts  as  can  only  be  discovered  by  our  senses. 

This  brings  us  to  a  second  charateristic  of  philo- 
sophical propositions,  namely,  that  they  must  be  a 
priori.  A  philosophical  proposition  must  be  such  as  can 
be  neither  proved  nor  disproved  by  empirical  evidence. 
Too  often  we  find  in  philosophical  books  arguments 
based  upon  the  course  of  history,  or  the  convolutions  of 
the  brain,  or  the  eyes  of  shell-fish.  Special  and  accidental 
facts  of  this  kind  are  irrelevant  to  philosophy,  which  must 
make  only  such  assertions  as  would  be  equally  true 
however  the  actual  world  were  constituted. 

We  may  sum  up  these  two  characteristics  of  philo- 
sophical propositions  by  saying  that  philosophy  is  the 
science  of  the  possible.  But  this  statement  unexplained 
is  liable  to  be  misleading,  since  it  may  be  thought  that 
the  possible  is  something  other  than  the  general,  whereas 
in  fact  the  two  are  indistinguishable. 

Philosophy,  if  what  has  been  said  is  correct,  becomes 
indistinguishable  from  logic  as  that  word  has  now  come 


112  MYSTICISM   AND   LOGIC 

to  be  used.  The  study  of  logic  consists,  broadly  speak- 
ing, of  two  not  very  sharply  distinguished  portions.  On 
the  one  hand  it  is  concerned  with  those  general  state- 
ments which  can  be  made  concerning  everything  without 
mentioning  any  one  thing  or  predicate  or  relation,  such 
for  example  as  "  if  x  is  a  member  of  the  class  a  and  every 
member  of  a  is  a  member  of  ft ,  then  %  is  a  member  of 
the  class  ft,  whatever  x,  a,  and  fi  may  be."  On  the  other 
hand,  it  is  concerned  with  the  analysis  and  enumeration 
of  logical  forms,  i.e.  with  the  kinds  of  propositions  that 
may  occur,  with  the  various  types  of  facts,  and  with  the 
classification  of  the  constituents  of  facts.  In  this  way 
logic  provides  an  inventory  of  possibilities,  a  repertory 
of  abstractly  tenable  hypotheses. 

It  might  be  thought  that  such  a  study  would  be  too 
vague  and  too  general  to  be  of  any  very  great  importance, 
and  that,  if  its  problems  became  at  any  point  sufficiently 
definite,  they  would  be  merged  in  the  problems  of  some 
special  science.  It  appears,  however,  that  this  is  not  the 
case.  In  some  problems,  for  example,  the  analysis  of 
space  and  time,  the  nature  of  perception,  or  the  theory 
of  judgment,  the  discovery  of  the  logical  form  of  the 
facts  involved  is  the  hardest  part  of  the  work  and  the 
part  whose  performance  has  been  most  lacking  hitherto. 
It  is  chiefly  for  want  of  the  right  logical  hypothesis  that 
such  problems  have  hitherto  been  treated  in  such  an  un- 
satisfactory manner,  and  have  given  rise  to  those  con- 
tradictions or  antinomies  in  which  the  enemies  of  reason 
among  philosophers  have  at  all  times  delighted. 

By  concentrating  attention  upon  the  investigation  of 
logical  forms,  it  becomes  possible  at  last  for  philosophy 
to  deal  with  its  problems  piecemeal,  and  to  obtain,  as 
the  sciences  do,  such  partial  and  probably  not  wholly 
correct  results  as  subsequent  investigation  can  utilise 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    113 

even  while  it  supplements  and  improves  them.  Most 
philosophies  hitherto  have  been  constructed  all  in  one 
block,  in  such  a  way  that,  if  they  were  not  wholly  correct, 
they  were  wholly  incorrect,  and  could  not  be  used  as  a 
basis  for  further  investigations.  It  is  chiefly  owing  to 
this  fact  that  philosophy,  unlike  science,  has  hitherto  been 
unprogressive,  because  each  original  philosopher  has  had 
to  begin  the  work  again  from  the  beginning,  without  being 
able  to  accept  anything  definite  from  the  work  of  his 
predecessors.  A  scientific  philosophy  such  as  I  wish  to 
recommend  will  be  piecemeal  and  tentative  like  other 
sciences  ;  above  all,  it  will  be  able  to  invent  hypotheses 
which,  even  if  they  are  not  wholly  true,  will  yet  remain 
fruitful  after  the  necessary  corrections  have  been  made. 
This  possibility  of  successive  approximations  to  the  truth 
is,  more  than  anything  else,  the  source  of  the  triumphs 
of  science,  and  to  transfer  this  possibility  to  philosophy 
is  to  ensure  a  progress  in  method  whose  importance 
it  would  be  almost  impossible  to  exaggerate. 

The  essence  of  philosophy  as  thus  conceived  is  analy- 
sis, not  synthesis.  To  build  up  systems  of  the  world,  like 
Heine's  German  professor  who  knit  together  fragments  of 
life  and  made  an  intelligible  system  out  of  them,  is  not, 
I  believe,  any  more  feasible  than  the  discovery  of  the 
philosopher's  stone.  What  is  feasible  is  the  understanding 
of  general  forms,  and  the  division  of  traditional  problems 
into  a  number  of  separate  and  less  baffling  questions. 
"  Divide  and  conquer  "  is  the  maxim  of  success  here  as 
elsewhere. 

Let  us  illustrate  these  somewhat  general  maxims  by 
examining  their  application  to  the  philosophy  of  space, 
for  it  is  only  in  application  that  the  meaning  or  impor- 
tance of  a  method  can  be  understood.  Suppose  we  are 
confronted  with  the  problem  of  space  as  presented  in 


H4  MYSTICISM   AND   LOGIC 

Kant's  Transcendental  ^Esthetic,  and  suppose  we  wish 
to  discover  what  are  the  elements  of  the  problem  and 
what  hope  there  is  of  obtaining  a  solution  of  them.  It 
will  soon  appear  that  three  entirely  distinct  problems, 
belonging  to  different  studies,  and  requiring  different 
methods  for  their  solution,  have  been  confusedly  combined 
in  the  supposed  single  problem  with  which  Kant  is 
concerned.  There  is  a  problem  of  logic,  a  problem  of 
physics,  and  a  problem  of  theory  of  knowledge.  Of 
these  three,  the  problem  of  logic  can  be  solved  exactly 
and  perfectly  ;  the  problem  of  physics  can  probably  be 
solved  with  as  great  a  degree  of  certainty  and  as  great 
an  approach  to  exactness  as  can  be  hoped  in  an  empirical 
region  ;  the  problem  of  theory  of  knowledge,  however, 
remains  very  obscure  and  very  difficult  to  deal  with. 
Let  us  see  how  these  three  problems  arise. 

(i)  The  logical  problem  has  arisen  through  the 
suggestions  of  non-Euclidean  geometry.  Given  a  body 
of  geometrical  propositions,  it  is  not  difficult  to  find 
a  minimum  statement  of  the  axioms  from  which  this 
body  of  propositions  can  be  deduced.  It  is  also  not 
difficult,  by  dropping  or  altering  some  of  these  axioms, 
to  obtain  a  more  general  or  a  different  geometry,  having, 
from  the  point  of  view  of  pure  mathematics,  the  same 
logical  coherence  and  the  same  title  to  respect  as  the 
more  familiar  Euclidean  geometry.  The  Euclidean 
geometry  itself  is  true  perhaps  of  actual  space  (though 
this  is  doubtful),  but  certainly  of  an  infinite  number  of 
purely  arithmetical  systems,  each  of  which,  from  the 
point  of  view  of  abstract  logic,  has  an  equal  and  inde- 
feasible right  to  be  called  a  Euclidean  space.  Thus 
space  as  an  object  of  logical  or  mathematical  study  loses 
its  uniqueness  ;  not  only  are  there  many  kinds  of  spaces, 
but  there  are  an  infinity  of  examples  of  each  kind, 


SCIENTIFIC  METHOD  IN  PHILOSOPHY     115 

though  it  is  difficult  to  find  any  kind  of  which  the  space 
of  physics  may  be  an  example,  and  it  is  impossible  to 
find  any  kind  of  which  the  space  of  physics  is  certainly 
an  example.  As  an  illustration  of  one  possible  logical 
system  of  geometry  we  may  consider  all  relations  of 
three  terms  which  are  analogous  in  certain  formal  respects 
to  the  relation  "  between  "  as  it  appears  to  be  in  actual 
space.  A  space  is  then  defined  by  means  of  one  such 
three-term  relation.  The  points  of  the  space  are  all  the 
terms  which  have  this  relation  to  something  or  other, 
and  their  order  in  the  space  in  question  is  determined 
by  this  relation.  The  points  of  one  space  are  necessarily 
also  points  of  other  spaces,  since  there  are  necessarily 
other  three-term  relations  having  those  same  points  for 
their  field.  The  space  in  fact  is  not  determined  by  the 
class  of  its  points,  but  by  the  ordering  three-term  rela- 
tion. When  enough  abstract  logical  properties  of  such 
relations  have  been  enumerated  to  determine  the  resulting 
kind  of  geometry,  say,  for  example,  Euclidean  geometry, 
it  becomes  unnecessary  for  the  pure  geometer  in  his  ab- 
stract capacity  to  distinguish  between  the  various  relations 
which  have  all  these  properties.  He  considers  the  whole 
class  of  such  relations,  not  any  single  one  among  them. 
Thus  in  studying  a  given  kind  of  geometry  the  pure 
mathematician  is  studying  a  certain  class  of  relations 
defined  by  means  of  certain  abstract  logical  properties 
which  take  the  place  of  what  used  to  be  called  axioms. 
The  nature  of  geometrical  reasoning  therefore  is  purely 
deductive  and  purely  logical ;  if  any  special  epistemolo- 
gicai  peculiarities  are  to  be  found  in  geometry,  it  must 
not  be  in  the  reasoning,  but  in  our  knowledge  concerning 
the  axioms  in  some  given  space. 

(2)  The  physical  problem  of  space  is  both  more  in- 
teresting and  more  difficult  than  the  logical  problem. 


ii6  MYSTICISM   AND   LOGIC 

The  physical  problem  may  be  stated  as  follows  :  to  find 
in  the  physical  world,  or  to  construct  from  physical 
materials,  a  space  of  one  of  the  kinds  enumerated  by  the 
logical  treatment  of  geometry.  This  problem  derives 
its  difficulty  from  the  attempt  to  accommodate  to  the 
roughness  and  vagueness  of  the  real  world  some  system 
possessing  the  logical  clearness  and  exactitude  of  pure 
mathematics.  That  this  can  be  done  with  a  certain 
degree  of  approximation  is  fairly  evident  If  I  see  three 
people  A,  B,  and  C  sitting  in  a  row,  I  become  aware  of 
the  fact  which  may  be  expressed  by  saying  that  B  is  be- 
tween A  and  C  rather  than  that  A  is  between  B  and  C, 
or  C  is  between  A  and  B.  This  relation  of  "  between  " 
which  is  thus  perceived  to  hold  has  some  of  the  abstract 
logical  properties  of  those  three-term  relations  which, 
we  saw,  give  rise  to  a  geometry,  but  its  properties  fail  to 
be  exact,  and  are  not,  as  empirically  given,  amenable 
to  the  kind  of  treatment  at  which  geometry  aims.  In 
abstract  geometry  we  deal  with  points,  straight  lines,  and 
planes  ;  but  the  three  people  A,  B,  and  C  whom  I  see 
sitting  in  a  row  are  not  exactly  points,  nor  is  the  row 
exactly  a  straight  line.  Nevertheless  physics,  which 
formally  assumes  a  space  containing  points,  straight 
lines,  and  planes,  is  found  empirically  to  give  results 
applicable  to  the  sensible  world.  It  must  therefore  be 
possible  to  find  an  interpretation  of  the  points,  straight 
lines,  and  planes  of  physics  in  terms  of  physical  data,  or 
at  any  rate  in  terms  of  data  together  with  such  hypo- 
thetical additions  as  seem  least  open  to  question.  Since 
all  data  suffer  from  a  lack  of  mathematical  precision 
through  being  oi  a  certain  size  and  somewhat  vague  in 
outline,  it  is  plain  that  if  such  a  notion  as  that  of  a  point 
is  to  find  any  application  to  empirical  material,  the  point 
must  be  neither  a  datum  nor  a  hypothetical  addition  to 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    117 

data,  but  a  construction  by  means  of  data  with  their 
hypothetical  additions.  It  is  obvious  that  any  hypo- 
thetical filling  out  of  data  is  less  dubious  and  unsatis- 
factory when  the  additions  are  closely  analogous  to  data 
than  when  they  are  of  a  radically  different  sort.  To 
assume,  for  example,  that  objects  which  we  see  continue, 
after  we  have  turned  away  our  eyes,  to  be  more  or  less 
analogous  to  what  they  were  while  we  were  looking,  is 
a  less  violent  assumption  than  to  assume  that  such  objects 
are  composed  of  an  infinite  number  of  mathematical 
points.  Hence  in  the  physical  study  of  the  geometry 
of  physical  space,  points  must  not  be  assumed  ab  initio  as 
they  are  in  the  logical  treatment  of  geometry,  but  must 
be  constructed  as  systems  composed  of  data  and  hypo- 
thetical analogues  of  data.  We  are  thus  led  naturally 
to  define  a  physical  point  as  a  certain  class  of  those 
objects  which  are  the  ultimate  constituents  of  the  physical 
world.  It  will  be  the  class  of  all  those  objects  which,  as 
one  would  naturally  say,  contain  the  point.  To  secure  a 
definition  giving  this  result,  without  previously  assuming 
that  physical  objects  are  composed  of  points,  is  an  agree- 
able problem  in  mathematical  logic.  The  solution  of 
this  problem  and  the  perception  of  its  importance  are 
due  to  my  friend  Dr.  Whitehead.  The  oddity  of  regard- 
ing a  point  as  a  class  of  physical  entities  wears  off  with 
familiarity,  and  ought  in  any  case  not  to  be  felt  by  those 
who  maintain,  as  practically  every  one  does,  that  points 
are  mathematical  fictions.  The  word  "  fiction  "  is  used 
glibly  in  such  connexions  by  many  men  who  seem  not 
to  feel  the  necessity  of  explaining  how  it  can  come  about 
that  a  fiction  can  be  so  useful  in  the  study  of  the  actual 
world  as  the  points  of  mathematical  physics  have  been 
found  to  be.  By  our  definition,  which  regards  a  point 
as  a  class  of  physical  objects,  it  is  explained  both  how 


n8  MYSTICISM   AND   LOGIC 

the  use  of  points  can  lead  to  important  physical  results, 
and  how  we  can  nevertheless  avoid  the  assumption  that 
points  are  themselves  entities  in  the  physical  world. 

Many  of  the  mathematically  convenient  properties  of 
abstract  logical  spaces  cannot  be  either  known  to  belong 
or  known  not  to  belong  to  the  space  of  physics.  Such 
are  all  the  properties  connected  with  continuity.  For 
to  know  that  actual  space  has  these  properties  would 
require  an  infinite  exactness  of  sense-perception.  If 
actual  space  is  continuous,  there  are  nevertheless  many 
possible  non-continuous  spaces  which  will  be  empirically 
indistinguishable  from  it ;  and,  conversely,  actual  space 
may  be  non-continuous  and  yet  empirically  indistinguish- 
able from  a  possible  continuous  space.  Continuity, 
therefore,  though  obtainable  in  the  a  priori  region  of 
arithmetic,  is  not  with  certainty  obtainable  in  the  space 
or  time  of  the  physical  world  :  whether  these  are  con- 
tinuous or  not  would  seem  to  be  a  question  not  only 
unanswered  but  for  ever  unanswerable.  From  the  point 
of  view  of  philosophy,  however,  the  discovery  that 
a  question  is  unanswerable  is  as  complete  an  answer  as 
any  that  could  possibly  be  obtained.  And  from  the 
point  of  view  of  physics,  where  no  empirical  means  of 
distinction  can  be  found,  there  can  be  no  empirical 
objection  to  the  mathematically  simplest  assumption, 
which  is  that  of  continuity. 

The  subject  of  the  physical  theory  of  space  is  a  very 
large  one,  hitherto  little  explored.  It  is  associated  with 
a  similar  theory  of  time,  and  both  have  been  forced  upon 
the  attention  of  philosophically  minded  physicists  by  the 
discussions  which  have  raged  concerning  the  theory  of 
relativity. 

(3)  The  problem  with  which  Kant  is  concerned  in  the 
Transcendental  Esthetic  is  primarily  the  epistemological 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    119 

problem  :  "  How  do  we  come  to  have  knowledge  of 
geometry  a  priori  ?  "  By  the  distinction  between  the 
logical  and  physical  problems  of  geometry,  the  bearing 
and  scope  of  this  question  are  greatly  altered.  Our 
knowledge  of  pure  geometry  is  a  priori  but  is  wholly 
logical.  Our  knowledge  of  physical  geometry  is  synthetic, 
but  is  not  a  priori.  Our  knowledge  of  pure  geometry 
is  hypothetical,  and  does  not  enable  us  to  assert,  for 
example,  that  the  axiom  of  parallels  is  true  in  the  physical 
world.  Our  knowledge  of  physical  geometry,  while  it 
does  enable  us  to  assert  that  this  axiom  is  approximately 
verified,  does  not,  owing  to  the  inevitable  inexactitude 
of  observation,  enable  us  to  assert  that  it  is  verified 
exactly.  Thus,  with  the  separation  which  we  have  made 
between  pure  geometry  and  the  geometry  of  physics,  the 
Kantian  problem  collapses.  To  the  question,  "  How 
is  synthetic  a  priori  knowledge  possible  ?  "  we  can 
now  reply,  at  any  rate  so  far  as  geometry  is  concerned, 
"It  is  not  possible,"  if  "synthetic"  means  "not  de- 
ducible  from  logic  alone."  Our  knowledge  of  geometry, 
like  the  rest  of  our  knowledge,  is  derived  partly  from 
logic,  partly  from  sense,  and  the  peculiar  position  which 
in  Kant's  day  geometry  appeared  to  occupy  is  seen  now 
to  be  a  delusion.  There  are  still  some  philosophers,  it  is 
true,  who  maintain  that  our  knowledge  that  the  axiom  of 
parallels,  for  example,  is  true  of  actual  space,  is  not  to 
be  accounted  for  empirically,  but  is  as  Kant  maintained 
derived  from  an  a  priori  intuition.  This  position  is  not 
logically  refutable,  but  I  think  it  loses  all  plausibility  as 
soon  as  we  realise  how  complicated  and  derivative  is 
the  notion  of  physical  space.  As  we  have  seen,  the 
application  of  geometry  to  the  physical  world  in  no  way 
demands  that  there  should  really  be  points  and  straight 
lines  among  physical  entities.  The  principle  of  economy, 


120  MYSTICISM   AND   LOGIC 

therefore,  demands  that  we  should  abstain  from  assum- 
ing the  existence  of  points  and  straight  lines.  As  soon, 
however,  as  we  accept  the  view  that  points  and  straight 
lines  are  complicated  constructions  by  means  of  classes 
of  physical  entities,  the  hypothesis  that  we  have  an 
a  priori  intuition  enabling  us  to  know  what  happens  to 
straight  lines  when  they  are  produced  indefinitely  becomes 
extremely  strained  and  harsh  ;  nor  do  I  think  that  such 
an  hypothesis  would  ever  have  arisen  in  the  mind  of  a 
philosopher  who  had  grasped  the  nature  of  physical 
space.  Kant,  under  the  influence  of  Newton,  adopted, 
though  with  some  vacillation,  the  hypothesis  of  absolute 
space,  and  this  hypothesis,  though  logically  unobjection- 
able, is  removed  by  Occam's  razor,  since  absolute  space 
is  an  unnecessary  entity  in  the  explanation  of  the  physical 
world.  Although,  therefore,  we  cannot  refute  the  Kantian 
theory  of  an  a  priori  intuition,  we  can  remove  its  grounds 
one  by  one  through  an  analysis  of  the  problem .  Thus,  here 
as  in  many  other  philosophical  questions,  the  analytic 
method,  while  not  capable  of  arriving  at  a  demonstrative 
result,  is  nevertheless  capable  of  showing  that  all  the 
positive  grounds  in  favour  of  a  certain  theory  are  fallacious 
and  that  a  less  unnatural  theory  is  capable  of  accounting 
for  the  facts. 

Another  question  by  which  the  capacity  of  the  analytic 
method  can  be  shown  is  the  question  of  realism.  Both 
those  who  advocate  and  those  who  combat  realism  seem 
to  me  to  be  far  from  clear  as  to  the  nature  of  the  problem 
which  they  are  discussing.  If  we  ask  :  "  Are  our  objects 
of  perception  real  and  are  they  independent  of  the  per- 
cipient ?  "  it  must  be  supposed  that  we  attach  some 
meaning  to  the  words  "  real "  and  "  independent,"  and 
yet,  if  either  side  in  the  controversy  of  realism  is 
asked  to  define  these  two  words,  their  answer  is  pretty 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    121 

sure  to  embody  confusions  such  as  logical  analysis  will 
reveal. 

Let  us  begin  with  the  word  "  real."  There  certainly  are 
objects  of  perception,  and  therefore,  if  the  question 
whether  these  objects  are  real  is  to  be  a  substantial 
question,  there  must  be  in  the  world  two  sorts  of  objects, 
namely,  the  real  and  the  unreal,  and  yet  the  unreal  is 
supposed  to  be  essentially  what  there  is  not.  The  question 
what  properties  must  belong  to  an  object  in  order  to 
make  it  real  is  one  to  which  an  adequate  answer  is  seldom 
if  ever  forthcoming.  There  is  of  course  the  Hegelian 
answer,  that  the  real  is  the  self-consistent  and  that  noth- 
ing is  self-consistent  except  the  Whole ;  but  this  answer, 
true  or  false,  is  not  relevant  in  our  present  discussion, 
which  moves  on  a  lower  plane  and  is  concerned  with  the 
status  of  objects  of  perception  among  other  objects  of 
equal  fragmentariness.  Objects  of  perception  are  con- 
trasted, in  the  discussions  concerning  realism,  rather  with 
psychical  states  on  the  one  hand  and  matter  on  the  other 
hand  than  with  the  all-inclusive  whole  of  things.  The 
question  we  have  therefore  to  consider  is  the  question 
as  to  what  can  be  meant  by  assigning  "  reality  "  to  some 
but  not  all  of  the  entities  that  make  up  the  world.  Two 
elements,  I  think,  make  up  what  is  felt  rather  than  thought 
when  the  word  "  reality  "  is  used  in  this  sense.  A  thing 
is  real  if  it  persists  at  times  when  it  is  not  perceived  ;  or 
again,  a  thing  is  real  when  it  is  correlated  with  other  things 
in  a  way  which  experience  has  led  us  to  expect.  It  will 
be  seen  that  reality  in  either  of  these  senses  is  by  no 
means  necessary  to  a  thing,  and  that  in  fact  there  might 
be  a  whole  world  in  which  nothing  was  real  in  either  of 
these  senses.  It  might  turn  out  that  the  objects  of  per- 
ception failed  of  reality  in  one  or  both  of  these  respects, 
without  its  being  in  any  way  deducible  that  they  are 


122  MYSTICISM   AND   LOGIC 

not  parts  of  the  external  world  with  which  physics  deals. 
Similar  remarks  will  apply  to  the  word  "independent." 
Most  of  the  associations  of  this  word  are  bound  up  with 
ideas  as  to  causation  which  it  is  not  now  possible  to 
maintain.  A  is  independent  of  B  when  B  is  not  an 
indispensable  part  of  the  cause  of  A.  But  when  it  is 
recognised  that  causation  is  nothing  more  than  correla- 
tion, and  that  there  are  correlations  of  simultaneity  as 
well  as  of  succession,  it  becomes  evident  that  there  is 
no  uniqueness  in  a  series  of  casual  antecedents  of  a  given 
event,  but  that,  at  any  point  where  there  is  a  correlation 
of  simultaneity,  we  can  pass  from  one  line  of  antecedents 
to  another  in  order  to  obtain  a  new  series  of  causal 
antecedents.  It  will  be  necessary  to  specify  the  causal 
law  according  to  which  the  antecedents  are  to  be  con- 
sidered. I  received  a  letter  the  other  day  from  a  corre- 
spondent who  had  been  puzzled  by  various  philosophical 
questions.  After  enumerating  them  he  says  :  "  These 
questions  led  me  from  Bonn  to  Strassburg,  where  I  found 
Professor  Simmel."  Now,  it  would  be  absurd  to  deny 
that  these  questions  caused  his  body  to  move  from 
Bonn  to  Strassburg,  and  yet  it  must  be  supposed  that  a 
set  of  purely  mechanical  antecedents  could  also  be  found 
which  would  account  for  this  transfer  of  matter  from  one 
place  to  another.  Owing  to  this  plurality  of  causal  series 
antecedent  to  a  given  event,  the  notion  of  the  cause 
becomes  indefinite,  and  the  question  of  independence 
becomes  correspondingly  ambiguous.  Thus,  instead  of 
asking  simply  whether  A  is  independent  of  B,  we  ought 
to  ask  whether  there  is  a  series  determined  by  such  and 
such  causal  laws  leading  from  B  to  A.  This  point  is 
important  in  connexion  with  the  particular  question 
of  objects  of  perception.  It  may  be  that  no  objects  quite 
like  those  which  we  perceive  ever  exist  un  perceived ; 


SCIENTIFIC  METHOD  IN  PHILOSOPHY    123 

in  this  case  there  will  be  a  causal  law  according  to  which 
objects  of  perception  are  not  independent  of  being 
perceived.  But  even  if  this  be  the  case,  it  may  never- 
theless also  happen  that  there  are  purely  physical  causal 
laws  determining  the  occurrence  of  objects  which  are 
perceived  by  means  of  other  objects  which  perhaps  are 
not  perceived.  In  that  case,  in  regard  to  such  causal 
laws  objects  of  perception  will  be  independent  of  being 
perceived.  Thus  the  question  whether  objects  of  per- 
ception are  independent  of  being  perceived  is,  as  it 
stands,  indeterminate,  and  the  answer  will  be  yes  or  no 
according  to  the  method  adopted  of  making  it  determinate. 
I  believe  that  this  confusion  has  borne  a  very  large  part 
in  prolonging  the  controversies  on  this  subject,  which 
might  well  have  seemed  capable  of  remaining  for  ever 
undecided.  The  view  which  I  should  wish  to  advocate 
is  that  objects  of  perception  do  not  persist  unchanged 
at  times  when  they  are  not  perceived,  although  probably 
objects  more  or  less  resembling  them  do  exist  at  such 
times ;  that  objects  of  perception  are  part,  and  the  only 
empirically  knowable  part,  of  the  actual  subject-matter  of 
physics,  and  are  themselves  properly  to  be  called  physical ; 
that  purely  physical  laws  exist  determining  the  character 
and  duration  of  objects  of  perception  without  any 
reference  to  the  fact  that  they  are  perceived  ;  and  that 
in  the  establishment  of  such  laws  the  propositions  of 
physics  do  not  presuppose  any  propositions  of  psychology 
or  even  the  existence  of  mind.  I  do  not  know  whether 
realists  would  recognise  such  a  view  as  realism.  All 
that  I  should  claim  for  it  is,  that  it  avoids  difficulties 
which  seem  to  me  to  beset  both  realism  and  idealism  as 
hitherto  advocated,  and  that  it  avoids  the  appeal  which 
they  have  made  to  ideas  which  logical  analysis  shows 
to  be  ambiguous.  A  further  defence  and  elaboration  of 


124  MYSTICISM   AND   LOGIC 

the  positions  which  I  advocate,  but  for  which  time  is 
lacking  now,  will  be  found  indicated  in  my  book  on 
Our  Knowledge  of  the  External  World.1 

The  adoption  of  scientific  method  in  philosophy,  if 
I  am  not  mistaken,  compels  us  to  abandon  the  hope  of 
solving  many  of  the  more  ambitious  and  humanly 
interesting  problems  of  traditional  philosophy.  Some 
of  these  it  relegates,  though  with  little  expectation  of 
a  successful  solution,  to  special  sciences,  others  it  shows 
to  be  such  as  our  capacities  are  essentially  incapable  of 
solving.  But  there  remain  a  large  number  of  the  re- 
cognised problems  of  philosophy  in  regard  to  which  the 
method  advocated  gives  all  those  advantages  of  division 
into  distinct  questions,  of  tentative,  partial,  and  pro- 
gressive advance,  and  of  appeal  to  principles  with  which, 
independently  of  temperament,  all  competerit  students 
must  agree.  The  failure  of  philosophy  hitherto  has 
been  due  in  the  main  to  haste  aud  ambition  :  patience 
and  modesty,  here  as  in  other  sciences,  will  open  the 
road  to  solid  and  durable  progress. 

1  Open  Court  Company,  1914. 


VII 

THE   ULTIMATE  CONSTITUENTS 
OF   MATTER1 

I  WISH  to  discuss  in  this  article  no  less  a  question 
than  the  ancient  metaphysical  query,  "  What  is 
matter  ?  "  The  question,  "  What  is  matter  ?  "  in  so  far 
as  it  concerns  philosophy,  is,  I  think,  already  capable  of 
an  answer  which  in  principle  will  be  as  complete  as  an 
answer  can  hope  to  be  ;  that  is  to  say,  we  can  separate 
the  problem  into  an  essentially  soluble  and  an  essentially 
insoluble  portion,  and  we  can  now  see  how  to  solve  the 
essentially  soluble  portion,  at  least  as  regards  its  main 
outlines.  It  is  these  outlines  which  I  wish  to  suggest  in 
the  present  article.  My  main  position,  which  is  realistic, 
is,  I  hope  and  believe,  not  remote  from  that  of  Professor 
Alexander,  by  whose  writings  on  this  subject  I  have  profited 
greatly.2  It  is  also  in  close  accord  with  that  of  Dr.  Nunn.3 
Common  sense  is  accustomed  to  the  division  of  the 
world  into  mind  and  matter.  It  is  supposed  by  all  who 
have  never  studied  philosophy  that  the  distinction  be- 
tween mind  and  matter  is  perfectly  clear  and  easy,  that 
the  two  do  not  at  any  point  overlap,  and  that  only  a  fool 
or  a  philosopher  could  be  in  doubt  as  to  whether  any 
given  entity  is  mental  or  material.  This  simple  faith 

1  An  address  delivered  to  the  Philosophical  Society  of  Manchester 
in  February,  1915.  Reprinted  from  The  Monist,  July,  1915. 

1  Cf.  especially  Samuel  Alexander,  "  The  Basis  of  Realism,"  British 
Academy,  Vol.  VI. 

3  "  Are  Secondary  Qualities  Independent  of  Perception  ?  "  Proc. 
Arist.  Soc.,  1909-10,  pp.  191-218. 

125 


126  MYSTICISM   AND   LOGIC 

survives  in  Descartes  and  in  a  somewhat  modified  form 
in  Spinoza,  but  with  Leibniz  it  begins  to  disappear,  and 
from  his  day  to  our  own  almost  every  philosopher  of  note 
has  criticised  and  rejected  the  dualism  of  common  sense. 
It  is  my  intention  in  this  article  to  defend  this  dualism  ; 
but  before  defending  it  we  must  spend  a  few  moments  on 
the  reasons  which  have  prompted  its  rejection. 

Our  knowledge  of  the  material  world  is  obtained  by 
means  of  the  senses,  of  sight  and  touch  and  so  on.  At 
first  it  is  supposed  that  things  are  just  as  they  seem,  but 
two  opposite  sophistications  soon  destroy  this  naive 
belief.  On  the  one  hand  the  physicists  cut  up  matter 
into  molecules,  atoms,  corpuscles,  and  as  many  more 
such  subdivisions  as  their  future  needs  may  make  them 
postulate,  and  the  units  at  which  they  arrive  are  un- 
commonly different  from  the  visible,  tangible  objects  ot 
daily  life.  A  unit  of  matter  tends  more  and  more  to  be 
something  like  an  electromagnetic  field  filling  all  space, 
though  having  its  greatest  intensity  in  a  small  region. 
Matter  consisting  of  such  elements  is  as  remote  from 
daily  life  as  any  metaphysical  theory.  It  differs  from  the 
theories  of  metaphysicians  only  in  the  fact  that  its 
practical  efficacy  proves  that  it  contains  some  measure 
of  truth  and  induces  business  men  to  invest  money  on  the 
strength  of  it ;  but,  in  spite  of  its  connection  with  the  money 
market,  it  remains  a  metaphysical  theory  none  the  less. 

The  second  kind  of  sophistication  to  which  the  world 
of  common  sense  has  been  subjected  is  derived  from  the 
psychologists  and  physiologists.  The  physiologists  point 
out  that  what  we  see  depends  upon  the  eye,  that  what  we 
hear  depends  upon  the  ear,  and  that  all  our  senses  are 
liable  to  be  affected  by  anything  which  affects  the  brain, 
like  alcohol  or  hasheesh.  Psychologists  point  out  how 
much  of  what  we  think  we  see  is  supplied  by  association 


CONSTITUENTS   OF   MATTER  127 

or  unconscious  inference,  how  much  is  mental  inter- 
pretation, and  how  doubtful  is  the  residuum  which  can 
be  regarded  as  crude  datum.  From  these  facts  it  is 
argued  by  the  psychologists  that  the  notion  of  a  datum 
passively  received  by  the  mind  is  a  delusion,  and  it  is 
argued  by  the  physiologists  that  even  if  a  pure  datum  of 
sense  could  be  obtained  by  the  analysis  of  experience, 
still  this  datum  could  not  belong,  as  common  sense  sup- 
poses, to  the  outer  world,  since  its  whole  nature  is  con- 
ditioned by  our  nerves  and  sense  organs,  changing  as 
they  change  in  ways  which  it  is  thought  impossible  to 
connect  with  any  change  in  the  matter  supposed  to  be 
perceived.  This  physiologist's  argument  is  exposed  to 
the  rejoinder,  more  specious  than  solid,  that  our  know- 
ledge of  the  existence  of  the  sense  organs  and  nerves  is 
obtained  by  that  very  process  which  the  physiologist  has 
been  engaged  in  discrediting,  since  the  existence  of  the 
nerves  and  sense  organs  is  only  known  through  the 
evidence  of  the  senses  themselves.  This  argument  may 
prove  that  some  reinterpretation  of  the  results  of  phy- 
siology is  necessary  before  they  can  acquire  metaphysical 
validity.  But  it  does  not  upset  the  physiological  argu- 
ment in  so  far  as  this  constitutes  merely  a  reductio  ad 
absurdum  of  naive  realism. 

These  various  lines  of  argument  prove,  I  think,  that 
some  part  of  the  beliefs  of  common  sense  must  be  aban- 
doned. They  prove  that,  if  we  take  these  beliefs  as  a 
whole,  we  are  forced  into  conclusions  which  are  in  part 
self-contradictory  ;  but  such  arguments  cannot  of  them- 
selves decide  what  portion  of  our  common-sense  beliefs 
is  in  need  of  correction.  Common  sense  believes  that 
what  we  see  is  physical,  outside  the  mind,  and  continuing 
to  exist  if  we  shut  our  eyes  or  turn  them  in  another 
direction.  I  believe  that  common  sense  is  right  in 


128  MYSTICISM   AND   LOGIC 

regarding  what  we  see  as  physical  and  (in  one  of 
several  possible  senses)  outside  the  mind,  but  is 
probably  wrong  in  supposing  that  it  continues  to  exist 
when  we  are  no  longer  looking  at  it.  It  seems  to 
me  that  the  whole  discussion  of  matter  has  been  obscured 
by  two  errors  which  support  each  other.  The  first  of  these 
is  the  error  that  what  we  see,  or  perceive  through  any  of 
our  other  senses,  is  subjective  :  the  second  is  the  belief 
that  what  is  physical  must  be  persistent.  Whatever 
physics  may  regard  as  the  ultimate  constituents  of  matter, 
it  always  supposes  these  constituents  to  be  indestructible. 
Since  the  immediate  data  of  sense  are  not  indestructible 
but  in  a  state  of  perpetual  flux,  it  is  argued  that  these 
data  themselves  cannot  be  among  the  ultimate  con- 
stituents of  matter.  I  believe  this  to  be  a  sheer  mistake. 
The  persistent  particles  of  mathematical  physics  I  regard 
as  logical  constructions,  symbolic  fictions  enabling  us  to 
express  compendiously  very  complicated  assemblages  of 
facts  ;  and,  on  the  other  hand,  I  believe  that  the  actual 
data  in  sensation,  the  immediate  objects  of  sight  or  touch 
or  hearing,  are  extra-mental,  purely  physical,  and  among 
the  ultimate  constituents  of  matter. 

My  meaning  in  regard  to  the  impermanence  of  physical 
entities  may  perhaps  be  made  clearer  by  the  use  of  Berg- 
son's  favourite  illustration  of  the  cinematograph.  When 
I  first  read  Bergson's  statement  that  the  mathematician 
conceives  the  world  after  the  analogy  of  a  cinematograph, 
I  had  never  seen  a  cinematograph,  and  my  first  visit  to 
one  was  determined  by  the  desire  to  verify  Bergson's 
statement,  which  I  found  to  be  completely  true,  at  least 
so  far  as  I  am  concerned.  When,  in  a  picture  palace,  we 
see  a  man  rolling  down  hill,  or  running  away  from  the 
police,  or  falling  into  a  river,  or  doing  any  of  those  other 
things  to  which  men  in  such  places  are  addicted,  we  know 


CONSTITUENTS   OF   MATTER  129 

that  there  is  not  really  only  one  man  moving,  but  a  suc- 
cession of  films,  each  with  a  different  momentary  man. 
The  illusion  of  persistence  arises  only  through  the  ap- 
proach to  continuity  in  the  series  of  momentary  men. 
Now  what  I  wish  to  suggest  is  that  in  this  respect  the 
cinema  is  a  better  metaphysician  than  common  sense, 
physics,  or  philosophy.  The  real  man  too,  I  believe, 
however  the  police  may  swear  to  his  identity,  is  really  a 
series  of  momentary  men,  each  different  one  from  the 
other,  and  bound  together,  not  by  a  numerical  identity, 
but  by  continuity  and  certain  intrinsic  causal  laws.  And 
what  applies  to  men  applies  equally  to  tables  and  chairs, 
the  sun,  moon  and  stars.  Each  of  these  is  to  be  regarded, 
not  as  one  single  persistent  entity,  but  as  a  series  of 
entities  succeeding  each  other  in  time,  each  lasting  for  a 
very  brief  period,  though  probably  not  for  a  mere  mathe- 
matical instant.  In  saying  this  I  am  only  urging  the 
same  kind  of  division  in  time  as  we  are  accustomed  to 
acknowledge  in  the  case  of  space.  A  body  which  fills  a 
cubic  foot  will  be  admitted  to  consist  of  many  smaller 
bodies,  each  occupying  only  a  very  tiny  volume  ;  similarly 
a  thing  which  persists  for  an  hour  is  to  be  regarded  as 
composed  of  many  things  of  less  duration.  A  true  theory 
of  matter  requires  a  division  of  things  into  time-corpuscles 
as  well  as  into  space-corpuscles. 

The  world  may  be  conceived  as  consisting  of  a  multi- 
tude of  entities  arranged  in  a  certain  pattern.  The 
entities  which  are  arranged  I  shall  call  "  particulars." 
The  arrangement  or  pattern  results  from  relations  among 
particulars.  Classes  or  series  of  particulars,  collected  to- 
gether on  account  of  some  property  which  makes  it  con- 
venient to  be  able  to  speak  of  them  as  wholes,  are  what 
I  call  logical  constructions  or  symbolic  fictions.  The  par- 
ticulars are  to  be  conceived,  not  on  the  analogy  of  bricks 


130  MYSTICISM   AND   LOGIC 

in  a  building,  but  rather  on  the  analogy  of  notes  in  a 
symphony.  The  ultimate  constituents  of  a  symphony 
(apart  from  relations)  are  the  notes,  each  of  which  lasts 
only  for  a  very  short  time.  We  may  collect  together 
all  the  notes  played  by  one  instrument :  these  may  be 
regarded  as  the  analogues  of  the  successive  particulars 
which  common  sense  would  regard  as  successive  states  of 
one  "  thing."  But  the  "  thing  "  ought  to  be  regarded  as 
no  more  "  real "  or  "  substantial  "  than,  for  example, 
the  role  of  the  trombone.  As  soon  as  "  things  "  are  con- 
ceived in  this  manner  it  will  be  found  that  the  difficulties 
in  the  way  of  regarding  immediate  objects  of  sense  as 
physical  have  largely  disappeared. 

When  people  ask,  "  Is  the  object  of  sense  mental  or 
physical  ?  "  they  seldom  have  any  clear  idea  either  what 
is  meant  by  "  mental "  or  "  physical,"  or  what  criteria 
are  to  be  applied  for  deciding  whether  a  given  entity 
belongs  to  one  class  or  the  other.  I  do  not  know  how  to 
give  a  sharp  definition  of  the  word  "  mental,"  but  some- 
thing may  be  done  by  enumerating  occurrences  which  are 
indubitably  mental :  believing,  doubting,  wishing,  willing, 
being  pleased  or  pained,  are  certainly  mental  occurrences ; 
so  are  what  we  may  call  experiences,  seeing,  hearing, 
smelling,  perceiving  generally.  But  it  does  not  follow 
from  this  that  what  is  seen,  what  is  heard,  what  is  smelt, 
what  is  perceived,  must  be  mental.  When  I  see  a  flash 
of  lightning,  my  seeing  of  it  is  mental,  but  what  I  see, 
although  it  is  not  quite  the  same  as  what  anybody  else 
sees  at  the  same  moment,  and  although  it  seems  very 
unlike  what  the  physicist  would  describe  as  a  flash  of 
lightning,  is  not  mental.  I  maintain,  in  fact,  that  if  the 
physicist  could  describe  truly  and  fully  all  that  occurs  in 
the  physical  world  when  there  is  a  flash  of  lightning,  it 
would  contain  as  a  constituent  what  I  see,  and  also  what 


CONSTITUENTS   OF   MATTER  131 

is  seen  by  anybody  else  who  would  commonly  be  said  to 
see  the  same  flash.  What  I  mean  may  perhaps  be  made 
plainer  by  saying  that  if  my  body  could  remain  in 
exactly  the  same  state  in  which  it  is,  although  my  mind 
had  ceased  to  exist,  precisely  that  object  which  I  now  see 
when  I  see  the  flash  would  exist,  although  of  course  I 
should  not  see  it,  since  my  seeing  is  mental.  The  prin- 
cipal reasons  which  have  led  people  to  reject  this  view 
have,  I  think,  been  two  :  first,  that  they  did  not  ade- 
quately distinguish  between  my  seeing  and  what  I  see  ; 
secondly,  that  the  causal  dependence  of  what  I  see  upon 
my  body  has  made  people  suppose  that  what  I  see  can- 
not be  "  outside  "  me.  The  first  of  these  reasons  need 
not  detain  us,  since  the  confusion  only  needs  to  be 
pointed  out  in  order  to  be  obviated  ;  but  the  second 
requires  some  discussion,  since  it  can  only  be  answered 
by  removing  current  misconceptions,  on  the  one  hand  as 
to  the  nature  of  space,  and  on  the  other,  as  to  the  mean- 
ing of  causal  dependence. 

When  people  ask  whether  colours,  for  example,  or 
other  secondary  qualities  are  inside  or  outside  the  mind, 
they  seem  to  suppose  that  their  meaning  must  be  clear, 
and  that  it  ought  to  be  possible  to  say  yes  or  no  without 
any  further  discussion  of  the  terms  involved.  In  fact, 
however,  such  terms  as  "  inside  "  or  "  outside  "  are  very 
ambiguous.  What  is  meant  by  asking  whether  this  or 
that  is  "  in  "  the  mind  ?  The  mind  is  not  like  a  bag  or  a  pie ; 
it  does  not  occupy  a  certain  region  in  space,  or,  if  (in  a  sense) 
it  does,  what  is  in  that  region  is  presumably  part  of  the 
brain,  which  would  not  be  said  to  be  in  the  mind.  When 
people  say  that  sensible  qualities  are  in  the  mind,  they 
do  not  mean  "  spatially  contained  in  "  in  the  sense  in 
which  the  blackbirds  were  in  the  pie.  We  might  regard 
the  mind  as  an  assemblage  of  particulars,  namely,  what 


132  MYSTICISM   AND   LOGIC 

would  be  called  "  states  of  mind,"  which  would  belong 
together  in  virtue  of  some  specific  common  quality.  The 
common  quality  of  all  states  of  mind  would  be  the  quality 
designated  by  the  word  "  mental  "  ;  and  besides  this  we 
should  have  to  suppose  that  each  separate  person's 
states  of  mind  have  some  common  characteristic  distin- 
guishing them  from  the  states  of  mind  of  other  people. 
Ignoring  this  latter  point,  let  us  ask  ourselves  whether 
the  quality  designated  by  the  word  "  mental  "  does,  as  a 
matter  of  observation,  actually  belong  to  objects  of  sense, 
such  as  colours  or  noises.  I  think  any  candid  person 
must  reply  that,  however  difficult  it  may  be  to  know  what 
we  mean  by  "mental,"  it  is  not  difficult  to  see  that 
colours  and  noises  are  not  mental  in  the  sense  of  having 
that  intrinsic  peculiarity  which  belongs  to  beliefs  and 
wishes  and  volitions,  but  not  to  the  physical  world. 
Berkeley  advances  on  this  subject  a  plausible  argument1 
which  seems  to  me  to  rest  upon  an  ambiguity  in  the  word 
"  pain."  He  argues  that  the  realist  supposes  the  heat 
which  he  feels  in  approaching  a  fire  to  be  something 
outside  his  mind,  but  that  as  he  approaches  nearer  and 
nearer  to  the  fire  the  sensation  of  heat  passes  imper- 
ceptibly into  pain,  and  that  no  one  could  regard  pain  as 
something  outside  the  mind.  In  reply  to  this  argument, 
it  should  be  observed  in  the  first  place  that  the  heat  of 
which  we  are  immediately  aware  is  not  in  the  fire  but  in 
our  own  body.  It  is  only  by  inference  that  the  fire  is 
judged  to  be  the  cause  of  the  heat  which  we  feel  in  our 
body.  In  the  second  place  (and  this  is  the  more  im- 
portant point),  when  we  speak  of  pain  we  may  mean  one 
of  two  things  :  we  may  mean  the  object  of  the  sensation 
or  other  experience  which  has  the  quality  of  being  painful, 

1  First  dialogue  between  Hylas  and  Philonous,   Works  (Fraser's 
edition  1901),  I,  p.  384. 


CONSTITUENTS   OF   MATTER  133 

or  we  may  mean  the  quality  of  painfulness  itself.  When 
a  man  says  he  has  a  pain  in  his  great  toe,  what  he  means 
is  that  he  has  a  sensation  associated  with  his  great  toe 
and  having  the  quality  of  painfulness.  The  sensation 
itself,  like  every  sensation,  consists  in  experiencing  a 
sensible  object,  and  the  experiencing  has  that  quality  of 
painfulness  which  only  mental  occurrences  can  have,  but 
which  may  belong  to  thoughts  or  desires,  as  well  as  to 
sensations.  But  in  common  language  we  speak  of  the 
sensible  object  experienced  in  a  painful  sensation  as  a 
pain,  and  it  is  this  way  of  speaking  which  causes  the 
confusion  upon  which  the  plausibility  of  Berkeley's 
argument  depends.  It  would  be  absurd  to  attribute  the 
quality  of  painfulness  to  anything  non-mental,  and  hence 
it  comes  to  be  thought  that  what  we  call  a  pain  in  the  toe 
must  be  mental.  In  fact,  however,  it  is  not  the  sensible 
object  in  such  a  case  which  is  painful,  but  the  sensation, 
that  is  to  say,  the  experience  of  the  sensible  object.  As 
the  heat  which  we  experience  from  the  fire  grows  greater, 
the  experience  passes  gradually  from  being  pleasant  to 
being  painful,  but  neither  the  pleasure  nor  the  pain  is  a 
quality  of  the  object  experienced  as  opposed  to  the 
experience,  and  it  is  therefore  a  fallacy  to  argue  that  this 
object  must  be  mental  on  the  ground  that  painfulness  can 
only  be  attributed  to  what  is  mental. 

If,  then,  when  we  say  that  something  is  in  the  mind 
we  mean  that  it  has  a  certain  recognisable  intrinsic 
characteristic  such  as  belongs  to  thoughts  and  desires,  it 
must  be  maintained  on  grounds  of  immediate  inspection 
that  objects  of  sense  are  not  in  any  mind. 

A  different  meaning  of  "  in  the  mind  "  is,  however,  to 
be  inferred  from  the  arguments  advanced  by  those  who 
regard  sensible  objects  as  being  in  the  mind.  The  argu- 
ments used  are,  in  the  main,  such  as  would  prove  the 


134  MYSTICISM   AND   LOGIC 

causal  dependence  of  objects  of  sense  upon  the  percipient. 
Now  the  notion  of  causal  dependence  is  very  obscure  and 
difficult,  much  more  so  in  fact  than  is  generally  realised 
by  philosophers.  I  shall  return  to  this  point  in  a  moment. 
For  the  present,  however,  accepting  the  notion  of  causal 
dependence  without  criticism,  I  wish  to  urge  that  the 
dependence  in  question  is  rather  upon  our  bodies  than 
upon  our  minds.  The  visual  appearance  of  an  object  is 
altered  if  we  shut  one  eye,  or  squint,  or  look  previously 
at  something  dazzling  ;  but  all  these  are  bodily  acts,  and 
the  alterations  which  they  effect  are  to  be  explained  by 
physiology  and  optics,  not  by  psychology.1  They  are  in 
fact  of  exactly  the  same  kind  as  the  alterations  effected 
by  spectacles  or  a  microscope.  They  belong  therefore  to 
the  theory  of  the  physical  world,  and  can  have  no  bearing 
upon  the  question  whether  what  we  see  is  causally 
dependent  upon  the  mind.  What  they  do  tend  to  prove, 
and  what  I  for  my  part  have  no  wish  to  deny,  is  that  what 
we  see  is  causally  dependent  upon  our  body  and  is  not, 
as  crude  common  sense  would  suppose,  something  which 
would  exist  equally  if  our  eyes  and  nerves  and  brain 
were  absent,  any  more  than  the  visual  appearance  pre- 
sented by  an  object  seen  through  a  microscope  would  re- 
main if  the  microscope  were  removed.  So  long  as  it  is 
supposed  that  the  physical  world  is  composed  of  stable  and 
more  or  less  permanent  constituents,  the  fact  that  what  we 
see  is  changed  by  changes  in  our  body  appears  to  afford 
reason  for  regarding  what  we  see  as  not  an  ultimate  con- 
stituent of  matter.  But  if  it  is  recognised  that  the  ultimate 
constituents  of  matter  are  as  circumscribed  in  duration  as 
in  spatial  extent,  the  whole  of  this  difficulty  vanishes. 

There  remains,  however,  another  difficulty,  connected 
with  space.    When  we  look  at  the  sun  we  wish  to  know 

1  This  point  has  been  well  urged  by  the  American  realists. 


CONSTITUENTS  OF   MATTER  135 

something  about  the  sun  itself,  which  is  ninety-three 
million  miles  away  ;  but  what  we  see  is  dependent  upon 
our  eyes,  and  it  is  difficult  to  suppose  that  our  eyes  can 
affect  what  happens  at  a  distance  of  ninety-three  million 
miles.  Physics  tells  us  that  certain  electromagnetic 
waves  start  from  the  sun,  and  reach  our  eyes  after  about 
eight  minutes.  They  there  produce  disturbances  in  the 
rods  and  cones,  thence  in  the  optic  nerve,  thence  in  the 
brain.  At  the  end  of  this  purely  physical  series,  by  some 
odd  miracle,  comes  the  experience  which  we  call  "  seeing 
the  sun,"  and  it  is  such  experiences  which  form  the  whole 
and  sole  reason  for  our  belief  in  the  optic  nerve,  the  rods 
and  cones,  the  ninety-three  million  miles,  the  electro- 
magnetic waves,  and  the  sun  itself.  It  is  this  curious 
oppositeness  of  direction  between  the  order  of  causation 
as  affirmed  by  physics,  and  the  order  of  evidence  as 
revealed  by  theory  of  knowledge,  that  causes  the  most 
serious  perplexities  in  regard  to  the  nature  of  physical 
reality.  Anything  that  invalidates  our  seeing,  as  a  source 
of  knowledge  concerning  physical  reality,  invalidates  also 
the  whole  of  physics  and  physiology.  And  yet,  starting 
from  a  common-sense  acceptance  of  our  seeing,  physics  has 
been  led  step  by  step  to  the  construction  of  the  causal  chain 
in  which  our  seeing  is  the  last  link,  and  the  immediate 
object  which  we  see  cannot  be  regarded  as  that  initial  cause 
which  we  believe  to  be  ninety-three  million  miles  away,  and 
which  we  are  inclined  to  regard  as  the  "  real "  sun. 

I  have  stated  this  difficulty  as  forcibly  as  I  can,  be- 
cause I  believe  that  it  can  only  be  answered  by  a  radical 
analysis  and  reconstruction  of  all  the  conceptions  upon 
whose  employment  it  depends. 

Space,  time,  matter  and  cause,  are  the  chief  of  these 
conceptions.  Let  us  begin  with  the  conception  of  cause. 

Causal  dependence,  as  I  observed  a  moment  ago,  is  a 


136  MYSTICISM   AND   LOGIC 

conception  which  it  is  very  dangerous  to  accept  at  its  face 
value.  There  exists  a  notion  that  in  regard  to  any  event 
there  is  something  which  may  be  called  the  cause  of  that 
event — some  one  definite  occurrence,  without  which  the 
event  would  have  been  impossible  and  with  which  it  be- 
comes necessary.  An  event  is  supposed  to  be  dependent 
upon  its  cause  in  some  way  which  in  it  is  not  dependent 
upon  other  things.  Thus  men  will  urge  that  the  mind  is 
dependent  upon  the  brain,  or,  with  equal  plausibility,  that 
the  brain  is  dependent  upon  the  mind.  It  seems  not  im- 
probable that  if  we  had  sufficient  knowledge  we  could 
infer  the  state  of  a  man's  mind  from  the  state  of  his  brain, 
or  the  state  of  his  brain  from  the  state  of  his  mind.  So 
long  as  the  usual  conception  of  causal  dependence  is  re- 
tained, this  state  of  affairs  can  be  used  by  the  materialist 
to  urge  that  the  state  of  our  brain  causes  our  thoughts, 
and  by  the  idealist  to  urge  that  our  thoughts  cause  the 
state  of  our  brain.  Either  contention  is  equally  valid  or 
equally  invalid.  The  fact  seems  to  be  that  there  are  many 
correlations  of  the  sort  which  may  be  called  causal,  and 
that,  for  example,  either  a  physical  or  a  mental  event  can 
be  predicted,  theoretically,  either  from  a  sufficient  number 
of  physical  antecedents  or  from  a  sufficient  number  of 
mental  antecedents.  To  speak  of  the  cause  of  an  event  is 
therefore  misleading.  Any  set  of  antecedents  from  which 
the  event  can  theoretically  be  inferred  by  means  of  correla- 
tions might  be  called  a  cause  of  the  event.  But  to  speak  of 
the  cause  is  to  imply  a  uniqueness  which  does  not  exist. 

The  relevance  of  this  to  the  experience  which  we  call 
"  seeing  the  sun  "  is  obvious.  The  fact  that  there  exists 
a  chain  of  antecedents  which  makes  our  seeing  dependent 
upon  the  eyes  and  nerves  and  brain  does  not  even  tend  to 
show  that  there  is  not  another  chain  of  antecedents  in 
which  the  eyes  and  nerves  and  brain  as  physical  things 
are  ignored.  If  we  are  to  escape  from  the  dilemma  which 


CONSTITUENTS   OF   MATTER  137 

seemed  to  arise  out  of  the  physiological  causation  of  what 
we  see  when  we  say  we  see  the  sun,  we  must  find,  at  least 
in  theory,  a  way  of  stating  causal  laws  for  the  physical 
world,  in  which  the  units  are  not  material  things,  such  as 
the  eyes  and  nerves  and  brain,  but  momentary  particulars 
of  the  same  sort  as  our  momentary  visual  object  when  we 
look  at  the  sun.  The  sun  itself  and  the  eyes  and  nerves 
and  brain  must  be  regarded  as  assemblages  of  momentary 
particulars.  Instead  of  supposing,  as  we  naturally  do 
when  we  start  from  an  uncritical  acceptance  of  the 
apparent  dicta  of  physics,  that  matter  is  what  is  "  really 
real "  in  the  physical  world,  and  that  the  immediate 
objects  of  sense  are  mere  phantasms,  we  must  regard 
matter  as  a  logical  construction,  of  which  the  con- 
stituents will  be  just  such  evanescent  particulars  as 
may,  when  an  observer  happens  to  be  present,  become 
data  of  sense  to  that  observer.  What  physics  regards  as 
the  sun  of  eight  minutes  ago  will  be  a  whole  assemblage 
of  particulars,  existing  at  different  times,  spreading  out 
from  a  centre  with  the  velocity  of  light,  and  containing 
among  their  number  all  those  visual  data  which  are  seen 
by  people  who  are  now  looking  at  the  sun.  Thus  the  sun 
of  eight  minutes  ago  is  a  class  of  particulars,  and  what  I 
see  when  I  now  look  at  the  sun  is  one  member  of  this 
class.  The  various  particulars  constituting  this  class 
will  be  correlated  with  each  other  by  a  certain  continuity 
and  certain  intrinsic  laws  of  variation  as  we  pass  out- 
wards from  the  centre,  together  with  certain  modifica- 
tions correlated  extrinsically  with  other  particulars  which 
are  not  members  of  this  class.  It  is  these  extrinsic 
modifications  which  represent  the  sort  of  facts  that,  in 
our  former  account,  appeared  as  the  influence  of  the  eyes 
and  nerves  in  modifying  the  appearance  of  the  sun.1 

1  Cf .  T.  P.  Nunn,  "  Are  Secondary  Qualities  Independent  of  Per- 
ception ?  "  Pvoc.  A  fist.  Soc.,  1909-1910. 


138  MYSTICISM   AND   LOGIC 

The  prima  facie  difficulties  in  the  way  of  this  view  are 
chiefly  derived  from  an  unduly  conventional  theory  of 
space.  It  might  seem  at  first  sight  as  if  we  had  packed  the 
world  much  fuller  than  it  could  possibly  hold.  At  every 
place  between  us  and  the  sun,  we  said,  there  is  to  be  a 
particular  which  is  to  be  a  member  of  the  sun  as  it  was  a 
few  minutes  ago.  There  will  also,  of  course,  have  to  be  a 
particular  which  is  a  member  of  any  planet  or  fixed  star 
that  may  happen  to  be  visible  from  that  place.  At  the 
place  where  I  am,  there  will  be  particulars  which  will  be 
members  severally  of  all  the  "  things  "  I  am  now  said  to 
be  perceiving.  Thus  throughout  the  world,  everywhere, 
there  will  be  an  enormous  number  of  particulars  co- 
existing in  the  same  place.  But  these  troubles  result 
from  contenting  ourselves  too  readily  with  the  merely 
three-dimensional  space  to  which  schoolmasters  have 
accustomed  us.  The  space  of  the  real  world  is  a  space  of 
six  dimensions,  and  as  soon  as  we  realise  this  we  see  that 
there  is  plenty  of  room  for  all  the  particulars  for  which 
we  want  to  find  positions.  In  order  to  realise  this  we 
have  only  to  return  for  a  moment  from  the  polished  space 
of  physics  to  the  rough  and  untidy  space  of  our  immediate 
sensible  experience.  The  space  of  one  man's  sensible 
objects  is  a  three-dimensional  space.  It  does  not  appear 
probable  that  two  men  ever  both  perceive  at  the  same 
time  any  one  sensible  object ;  when  they  are  said  to  see 
the  same  thing  or  hear  the  same  noise,  there  will  always 
be  some  difference,  however  slight,  between  the  actual 
shapes  seen  or  the  actual  sounds  heard.  If  this  is  so,  and 
if,  as  is  generally  assumed,  position  in  space  is  purely 
relative,  it  follows  that  the  space  of  one  man's  objects 
and  the  space  of  another  man's  objects  have  no  place  in 
common,  that  they  are  in  fact  different  spaces,  and  not 
merely  different  parts  of  one  space.  I  mean  by  this  that 
such  immediate  spatial  relations  as  are  perceived  to  hold 


CONSTITUENTS   OF   MATTER  139 

between  the  different  parts  of  the  sensible  space  perceived 
by  one  man,  do  not  hold  between  parts  of  sensible  spaces 
perceived  by  different  men.  There  are  therefore  a  multi- 
tude of  three-dimensional  spaces  in  the  world  :  there  are 
all  those  perceived  by  observers,  and  presumably  also 
those  which  are  not  perceived,  merely  because  no  observer 
is  suitably  situated  for  perceiving  them. 

But  although  these  spaces  do  not  have  to  one  another 
the  same  kind  of  spatial  relations  as  obtain  between  the 
parts  of  one  of  them,  it  is  nevertheless  possible  to  arrange 
these  spaces  themselves  in  a  three-dimensional  order. 
This  is  done  by  means  of  the  correlated  particulars  which 
we  regard  as  members  (or  aspects)  of  one  physical  thing. 
When  a  number  of  people  are  said  to  see  the  same  object, 
those  who  would  be  said  to  be  near  to  the  object  see  a 
particular  occupying  a  larger  part  of  their  field  of  vision 
than  is  occupied  by  the  corresponding  particular  seen  by 
people  who  would  be  said  to  be  farther  from  the  thing. 
By  means  of  such  considerations  it  is  possible,  in  ways 
which  need  not  now  be  further  specified,  to  arrange  all 
the  different  spaces  in  a  three-dimensional  series.  Since 
each  of  the  spaces  is  itself  three-dimensional,  the  whole 
world  of  particulars  is  thus  arranged  in  a  six-dimensional 
space,  that  is  to  say,  six  co-ordinates  will  be  required  to 
assign  completely  the  position  of  any  given  particular, 
namely,  three  to  assign  its  position  in  its  own  space  and 
three  more  to  assign  the  position  of  its  space  among  the 
other  spaces. 

There  are  two  ways  of  classifying  particulars  :  we  may 
take  together  all  those  that  belong  to  a  given  "  perspec- 
tive," or  all  those  that  are,  as  common  sense  would  say, 
different  "  aspects  "  of  the  same  "  thing."  For  example, 
if  I  am  (as  is  said)  seeing  the  sun,  what  I  see  belongs  to 
two  assemblages  :  (i)  the  assemblage  of  all  my  present 
objects  of  sense,  which  is  what  I  call  a  "  perspective  "  ; 


MYSTICISM   AND   LOGIC 

(2)  the  assemblage  of  all  the  different  particulars  which 
would  be  called  aspects  of  the  sun  of  eight  minutes 
ago — this  assemblage  is  what  I  define  as  being  the  sun  of 
eight  minutes  ago.  Thus  "  perspectives  "  and  "  things  " 
are  merely  two  different  ways  of  classifying  particulars.  It 
is  to  be  observed  that  there  is  no  a  priori  necessity  for 
particulars  to  be  susceptible  of  this  double  classification. 
There  may  be  what  might  be  called  "  wild  "  particulars, 
not  having  the  usual  relations  by  which  the  classification 
is  effected ;  perhaps  dreams  and  hallucinations  are 
composed  of  particulars  which  are  "  wild  "  in  this  sense. 

The  exact  definition  of  what  is  meant  by  a  perspective 
is  not  quite  easy.  So  long  as  we  confine  ourselves  to 
visible  objects  or  to  objects  of  touch  we  might  define  the 
perspective  of  a  given  particular  as  "  all  particulars  which 
have  a  simple  (direct)  spatial  relation  to  the  given  par- 
ticular." Between  two  patches  of  colour  which  I  see 
now,  there  is  a  direct  spatial  relation  which  I  equally  see. 
But  between  patches  of  colour  seen  by  different  men 
there  is  only  an  indirect  constructed  spatial  relation  by 
means  of  the  placing  of  "  things  "  in  physical  space 
(which  is  the  same  as  the  space  composed  of  perspec- 
tives). Those  particulars  which  have  direct  spatial 
relations  to  a  given  particular  will  belong  to  the  same 
perspective.  But  if,  for  example,  the  sounds  which  I 
hear  are  to  belong  to  the  same  perspective  with  the 
patches  of  colour  which  I  see,  there  must  be  particulars 
which  have  no  direct  spatial  relation  and  yet  belong  to 
the  same  perspective.  We  cannot  define  a  perspective 
as  all  the  data  of  one  percipient  at  one  time,  because  we 
wish  to  allow  the  possibility  of  perspectives  which  are 
not  perceived  by  any  one.  There  will  be  need,  therefore, 
in  defining  a  perspective,  of  some  principle  derived 
neither  from  psychology  nor  from  space. 

Such  a  principle  may  be  obtained  from  the  considera- 


CONSTITUENTS   OF   MATTER  141 

tion  of  time.  The  one  all-embracing  time,  like  the  one 
all-embracing  space,  is  a  construction  ;  there  is  no  direct 
time-relation  between  particulars  belonging  to  my  per- 
spective and  particulars  belonging  to  another  man's.  On 
the  other  hand,  any  two  particulars  of  which  I  am  aware 
are  either  simultaneous  or  successive,  and  their  simul- 
taneity or  successiveness  is  sometimes  itself  a  datum  to 
me.  We  may  therefore  define  the  perspective  to  which  a 
given  particular  belongs  as  "  all  particulars  simultaneous 
with  the  given  particular,"  where  "  simultaneous  "  is  to 
be  understood  as  a  direct  simple  relation,  not  the  deriva- 
tive constructed  relation  of  physics.  It  may  be  observed 
that  the  introduction  of  "  local  time  "  suggested  by  the 
principle  of  relativity  has  effected,  for  purely  scientific 
reasons,  much  the  same  multiplication  of  times  as  we 
have  just  been  advocating. 

The  sum-total  of  all  the  particulars  that  are  (directly) 
either  simultaneous  with  or  before  or  after  a  given  par- 
ticular may  be  defined  as  the  "  biography  "  to  which  that 
particular  belongs.  It  will  be  observed  that,  just  as  a 
perspective  need  not  be  actually  perceived  by  any  one, 
so  a  biography  need  not  be  actually  lived  by  any  one. 
Those  biographies  that  are  lived  by  no  one  are  called 
"  official." 

The  definition  of  a  "  thing  "  is  effected  by  means  of 
continuity  and  of  correlations  which  have  a  certain 
differential  independence  of  other  "  things."  That  is  to 
say,  given  a  particular  in  one  perspective,  there  will 
usually  in  a  neighbouring  perspective  be  a  very  similar 
particular,  differing  from  the  given  particular,  to  the  first 
order  of  small  quantities,  according  to  a  law  involving 
only  the  difference  of  position  of  the  two  perspectives  in 
perspective  space,  and  not  any  of  the  other  "  things  "  in 
the  universe.  It  is  this  continuity  and  differential  in- 
dependence in  the  law  of  change  as  we  pass  from  one 


142  MYSTICISM   AND  LOGIC 

perspective  to  another  that  defines  the  class  of  particulars 
which  is  to  be  called  "  one  thing." 

Broadly  speaking,  we  may  say  that  the  physicist  finds 
it  convenient  to  classify  particulars  into  "  things,"  while 
the  psychologist  finds  it  convenient  to  classify  them  into 
"  perspectives  "  and  "  biographies,"  since  one  perspective 
may  constitute  the  momentary  data  of  one  percipient,  and 
one  biography  may  constitute  the  whole  of  the  data  of 
one  percipient  throughout  his  life. 

We  may  now  sum  up  our  discussion.  Our  object  has 
been  to  discover  as  far  as  possible  the  nature  of  the 
ultimate  constituents  of  the  physical  world.  When  I 
speak  of  the  "  physical  world,"  I  mean,  to  begin  with, 
the  world  dealt  with  by  physics.  It  is  obvious  that 
physics  is  an  empirical  science,  giving  us  a  certain  amount 
of  knowledge  and  based  upon  evidence  obtained  through 
the  senses.  But  partly  through  the  development  of 
physics  itself,  party  through  arguments  derived  from 
physiology,  psychology  or  metaphysics,  it  has  come  to 
be  thought  that  the  immediate  data  of  sense  could  not 
themselves  form  part  of  the  ultimate  constituents  of  the 
physical  world,  but  were  in  some  sense  "  mental,"  "  in 
the  mind,"  or  "  subjective."  The  grounds  for  this  view, 
in  so  far  as  they  depend  upon  physics,  can  only  be  ade- 
quately dealt  with  by  rather  elaborate  constructions 
depending  upon  symbolic  logic,  showing  that  out  of  such 
materials  as  are  provided  by  the  senses  it  is  possible  to 
construct  classes  and  series  having  the  properties  which 
physics  assigns  to  matter.  Since  this  argument  is  diffi- 
cult and  technical,  I  have  not  embarked  upon  it  in  this 
article.  But  in  so  far  as  the  view  that  sense-data  are 
"  mental "  rests  upon  physiology,  psychology,  or  meta- 
physics, I  have  tried  to  show  that  it  rests  upon  con- 
fusions and  prejudices — prejudices  in  favour  of  per- 
manence in  the  ultimate  constituents  of  matter,  and 


CONSTITUENTS  OF   MATTER  143 

confusions  derived  from  unduly  simple  notions  as  to 
space,  from  the  causal  correlation  of  sense-data  with 
sense-organs,  and  from  failure  to  distinguish  between 
sense-data  and  sensations.  If  what  we  have  said  on 
these  subjects  is  valid,  the  existence  of  sense-data  is 
logically  independent  of  the  existence  of  mind,  and  is 
causally  dependent  upon  the  body  of  the  percipient  rather 
than  upon  his  mind.  The  causal  dependence  upon  the 
body  of  the  percipient,  we  found,  is  a  more  complicated 
matter  than  it  appears  to  be,  and,  like  all  causal  depend- 
ence, is  apt  to  give  rise  to  erroneous  beliefs  through  mis- 
conceptions as  to  the  nature  of  causal  correlation.  If  we 
have  been  right  in  our  contentions,  sense-data  are  merely 
those  among  the  ultimate  constituents  of  the  physical 
world,  of  which  we  happen  to  be  immediately  aware ; 
they  themselves  are  purely  physical,  and  all  that  is  mental 
in  connection  with  them  is  our  awareness  of  them,  which 
is  irrelevant  to  their  nature  and  to  their  place  in  physics. 
Unduly  simple  notions  as  to  space  have  been  a  great 
stumbling-block  to  realists.  When  two  men  look  at  the 
same  table,  it  is  supposed  that  what  the  one  sees  and 
what  the  other  sees  are  in  the  same  place.  Since  the 
shape  and  colour  are  not  quite  the  same  for  the  two  men, 
this  raises  a  difficulty,  hastily  solved,  or  rather  covered 
up,  by  declaring  what  each  sees  to  be  purely  "  sub- 
jective " — though  it  would  puzzle  those  who  use  this  glib 
word  to  say  what  they  mean  by  it.  The  truth  seems  to 
be  that  space — and  time  also — is  much  more  complicated 
than  it  would  appear  to  be  from  the  finished  structure  of 
physics,  and  that  the  one  all-embracing  three-dimensional 
space  is  a  logical  construction,  obtained  by  means  of 
correlations  from  a  crude  space  of  six  dimensions.  The 
particulars  occupying  this  six-dimensional  space,  classi- 
fied in  one  way,  form  "  things,"  from  which  with  certain 
further  manipulations  we  can  obtain  what  physics  can 


144  MYSTICISM   AND   LOGIC 

regard  as  matter ;  classified  in  another  way,  they  form 
"  perspectives "  and  "  biographies/'  which  may,  if  a 
suitable  percipient  happens  to  exist,  form  respectively 
the  sense-data  of  a  momentary  or  of  a  total  experience. 
It  is  only  when  physical  "  things  "  have  been  dissected 
into  series  of  classes  of  particulars,  as  we  have  done,  that 
the  conflict  between  the  point  of  view  of  physics  and  the 
point  of  view  of  psychology  can  be  overcome.  This  con- 
flict, if  what  has  been  said  is  not  mistaken,  flows  from 
different  methods  of  classification,  and  vanishes  as  soon 
as  its  source  is  discovered. 

In  favour  of  the  theory  which  I  have  briefly  outlined, 
I  do  not  claim  that  it  is  certainly  true.  Apart  from  the 
likelihood  of  mistakes,  much  of  it  is  avowedly  hypo- 
thetical. What  I  do  claim  for  the  theory  is  that  it  may 
be  true,  and  that  this  is  more  than  can  be  said  for  any 
other  theory  except  the  closely  analogous  theory  of 
Leibriz.  The  difficulties  besetting  realism,  the  con- 
fusion obstructing  any  philosophical  account  of  physics, 
the  dili-mma  resulting  from  discrediting  sense-data, 
which  yet  remain  the  sole  source  of  our  knowledge  of  the 
outer  rorld — all  these  are  avoided  by  the  theory  which  I 
advor.-tt .  This  does  not  prove  the  theory  to  be  true, 
since  obably  many  other  theories  might  be  invented 
whiclf  would  havt-  the  same  merits.  But  it  does  prove 
that  the  .  <  ory  hap  a  better  chance  of  being  true  than 
any  ol  its  *  sent  competitors,  and  it  suggests  that  what 
can  be  knovn  with  certainty  is  likely  to  be  discoverable 
by  taking  our  theory  as  a  starting-point,  and  gradually 
freeing  it  from  all  si  r  assumptions  as  seem  irrelevant, 
unnecessary,  o  luifo  -l.'.d.  On  these  grounds,  I  recom- 
mend it  to  attention  as  a  i  ypothesis  and  a  basis  for  further 
work,  though  not  as  I,?  ;lf  a  finished  or  adequate  solution 
of  the  problem  with  \v  .chit  deals. 


VIII 

THE    RELATION    OF    SENSE-DATA 
TO   PHYSICS 

I.   THE  PROBLEM   STATED 

PHYSICS  is  said  to  be  an  empirical  science,  based 
upon  observation  and  experiment. 

It  is  supposed  to  be  verifiable,  i.e.  capable  of  calcu- 
lating beforehand  results  subsequently  confirmed  by 
observation  and  experiment. 

What  can  we  learn  by  observation  and  experiment  ? 

Nothing,  so  far  as  physics  is  concerned,  except  imme- 
diate data  of  sense  :  certain  patches  of  colour,  sounds, 
tastes,  smells,  etc.,  with  certain  spatio-temporal  rela- 
tions. 

The  supposed  contents  of  the  physical  world  are  prima 
facie  very  different  from  these  :  molecules  have  no  colour, 
atoms  make  no  noise,  electrons  have  no  taste,  and  cor- 
puscles do  not  even  smell. 

If  such  objects  are  to  be  verified,  it  must  be  solely 
through  their  relation  to  sense-data  :  they  must  have 
some  kind  of  correlation  with  sense-data,  and  must  be 
verifiable  through  their  correlation  alone. 

But  how  is  the  correlation  itself  ascertained  ?  A  cor- 
relation can  only  be  ascertained  empirically  by  the  cor- 
related objects  being  constantly  found  together.  But  in 
our  case,  only  one  term  of  the  correlation,  namely,  the 
sensible  term,  is  ever  found  :  the  other  term  seems  essen- 
L  145 


146  MYSTICISM   AND   LOGIC 

tially  incapable  of  being  found.  Therefore,  it  would  seem, 
the  correlation  with  objects  of  sense,  by  which  physics  was 
to  be  verified,  is  itself  utterly  and  for  ever  un verifiable. 
There  are  two  ways  of  avoiding  this  result. 

(1)  We  may  say  that  we  know  some  principle  a  priori, 
without  the  need  of  empirical  verification,  e.g.  that  our 
sense-data  have  causes  other  than  themselves,  and  that 
something  can  be  known  about  these  causes  by  inference 
from  their  effects.    This  way  has  been  often  adopted  by 
philosophers.    It  may  be  necessary  to  adopt  this  way  to 
some  extent,  but  in  so  far  as  it  is  adopted  physics  ceases 
to  be  empirical  or  based  upon  experiment  and  observa- 
tion alone.    Therefore  this  way  is  to  be  avoided  as  much 
as  possible. 

(2)  We  may  succeed  in  actually  defining  the  objects  of 
physics  as  functions  of  sense-data.     Just  in  so  far  as 
physics  leads  to  expectations,  this  must  be  possible,  since 
we  can  only  expect  what  can  be  experienced.    And  in  so 
far  as  the  physical  state  of  affairs  is  inferred  from  sense- 
data,  it  must  be  capable  of  expression  as  a  function  of 
sense-data.    The  problem  of  accomplishing  this  expres- 
sion leads  to  much  interesting  logico-mathematical  work. 

In  physics  as  commonly  set  forth,  sense-data  appear 
as  functions  of  physical  objects  :  when  such-and-such 
waves  impinge  upon  the  eye,  we  see  such-and-such 
colours,  and  so  on.  But  the  waves  are  in  fact  inferred 
from  the  colours,  not  vice  versa.  Physics  cannot  be 
regarded  as  validly  based  upon  empirical  data  until  the 
waves  have  been  expressed  as  functions  of  the  colours 
and  other  sense-data. 

Thus  if  physics  is  to  be  verifiable  we  are  faced  with  the 
following  problem  :  Physics  exhibits  sense-data  as  func- 
tions of  physical  objects,  but  verification  is  only  possible 
if  physical  objects  can  be  exhibited  as  functions  of  sense- 


SENSE-DATA  AND   PHYSICS  147 

data.  We  have  therefore  to  solve  the  equations  giving 
sense-data  in  terms  of  physical  objects,  so  as  to  make 
them  instead  give  physical  objects  in  terms  of  sense- 
data. 

II.    CHARACTERISTICS   OF   SENSE-DATA 

When  I  speak  of  a  "  sense-datum,"  I  do  not  mean  the 
whole  of  what  is  given  in  sense  at  one  time.  I  mean 
rather  such  a  part  of  the  whole  as  might  be  singled  out 
by  attention  :  particular  patches  of  colour,  particular 
noises,  and  so  on.  There  is  some  difficulty  in  deciding 
what  is  to  be  considered  one  sense-datum  :  often  atten- 
tion causes  divisions  to  appear  where,  so  far  as  can  be 
discovered,  there  were  no  divisions  before.  An  observed 
complex  fact,  such  as  that  this  patch  of  red  is  to  the  left 
of  that  patch  of  blue,  is  also  to  be  regarded  as  a  datum 
from  our  present  point  of  view  :  epistemologically,  it 
does  not  differ  greatly  from  a  simple  sense-datum  as 
regards  its  function  in  giving  knowledge.  Its  logical 
structure  is  very  different,  however,  from  that  of  sense  : 
sense  gives  acquaintance  with  particulars,  and  is  thus  a 
two-term  relation  in  which  the  object  can  be  named  but 
not  asserted,  and  is  inherently  incapable  of  truth  or  false- 
hood, whereas  the  observation  of  a  complex  fact,  which 
may  be  suitably  called  perception,  is  not  a  two-term 
relation,  but  involves  the  prepositional  form  on  the 
object-side,  and  gives  knowledge  of  a  truth,  not  mere 
acquaintance  with  a  particular.  This  logical  difference, 
important  as  it  is,  is  not  very  relevant  to  our  present 
problem  ;  and  it  will  be  convenient  to  regard  data  of 
perception  as  included  among  sense-data  for  the  purposes 
of  this  paper.  It  is  to  be  observed  that  the  particulars 
which  are  constituents  of  a  datum  of  perception  are 
always  sense-data  in  the  strict  sense. 


148  MYSTICISM   AND   LOGIC 

Concerning  sense-data,  we  know  that  they  are  there 
while  they  are  data,  and  this  is  the  epistemological  basis 
of  all  our  knowledge  of  external  particulars.  (The  mean- 
ing of  the  word  "  external "  of  course  raises  problems 
which  will  concern  us  later.)  We  do  not  know,  except  by 
means  of  more  or  less  precarious  inferences,  whether  the 
objects  which  are  at  one  time  sense-data  continue  to 
exist  at  times  when  they  are  not  data.  Sense-data  at  the 
times  when  they  are  data  are  all  that  we  directly  and 
primitively  know  of  the  external  world  ;  hence  in  episte- 
mology  the  fact  that  they  are  data  is  all-important.  But 
the  fact  that  they  are  all  that  we  directly  know  gives,  of 
course,  no  presumption  that  they  are  all  that  there  is.  If 
we  could  construct  an  impersonal  metaphysic,  independent 
of  the  accidents  of  our  knowledge  and  ignorance,  the 
privileged  position  of  the  actual  data  would  probably 
disappear,  and  they  would  probably  appear  as  a  rather 
haphazard  selection  from  a  mass  of  objects  more  or  less 
like  them.  In  saying  this,  I  assume  only  that  it  is 
probable  that  there  are  particulars  with  which  we  are 
not  acquainted.  Thus  the  special  importance  of  sense- 
data  is  in  relation  to  epistemology,  not  to  metaphysics. 
In  this  respect,  physics  is  to  be  reckoned  as  metaphysics  : 
it  is  impersonal,  and  nominally  pays  no  special  attention 
to  sense-data.  It  is  only  when  we  ask  how  physics  can 
be  known  that  the  importance  of  sense-data  re-emerges. 


III.   SENSIBILIA 

I  shall  give  the  name  sensibilia  to  those  objects  which 
have  the  same  metaphysical  and  physical  status  as  sense- 
data,  without  necessarily  being  data  to  any  mind.  Thus 
the  relation  of  a  sensibile  to  a  sense-datum  is  like  that  of 
a  man  to  a  husband  ;  a  man  becomes  a  husband  by 


SENSE-DATA  AND   PHYSICS  149 

entering  into  the  relation  of  marriage,  and  similarly  a 
sensibile  becomes  a  sense-datum  by  entering  into  the 
relation  of  acquaintance.  It  is  important  to  have  both 
terms  ;  for  we  wish  to  discuss  whether  an  object  which 
is  at  one  time  a  sense-datum  can  still  exist  at  a  time 
when  it  is  not  a  sense-datum.  We  cannot  ask  "  Can 
sense-data  exist  without  being  given  ?  "  for  that  is  like 
asking  "Can  husbands  exist  without  being  married?" 
We  must  ask  "  Can  sensibilia  exist  without  being  given  ?  " 
and  also  "Can  a  particular  sensibile  be  at  one  time  a 
sense-datum,  and  at  another  not  ?  "  Unless  we  have  the 
word  sensibile  as  well  as  the  word  "sense-datum,"  such 
questions  are  apt  to  entangle  us  in  trivial  logical  puzzles. 

It  will  be  seen  that  all  sense-data  are  sensibilia.  It  is 
a  metaphysical  question  whether  all  sensibilia  are  sense- 
data,  and  an  epistemological  question  whether  there 
exist  means  of  inferring  sensibilia  which  are  not  data 
from  those  that  are. 

A  few  preliminary  remarks,  to  be  amplified  as  we  pro- 
ceed, will  serve  to  elucidate  the  use  which  I  propose  to 
make  of  sensibilia. 

I  regard  sense-data  as  not  mental,  and  as  being,  in 
fact,  part  of  the  actual  subject-matter  of  physics.  There 
are  arguments,  shortly  to  be  examined,  for  their  sub- 
jectivity, but  these  arguments  seem  to  me  only  to  prove 
physiological  subjectivity,  i.e.  causal  dependence  on  the 
sense-organs,  nerves,  and  brain.  The  appearance  which 
a  thing  presents  to  us  is  causally  dependent  upon  these, 
in  exactly  the  same  way  as  it  is  dependent  upon  inter- 
vening fog  or  smoke  or  coloured  glass.  Both  dependences 
are  contained  in  the  statement  that  the  appearance 
which  a  piece  of  matter  presents  when  viewed  from  a 
given  place  is  a  function  not  only  of  the  piece  of  matter, 
but  also  of  the  intervening  medium.  (The  terms  used  in 


i5o  MYSTICISM   AND   LOGIC 

this  statement — "  matter,"  "  view  from  a  given  place," 
"  appearance,"  "  intervening  medium  " — will  all  be  de- 
fined in  the  course  of  the  present  paper.)  We  have  not 
the  means  of  ascertaining  how  things  appear  from  places 
not  surrounded  by  brain  and  nerves  and  sense-organs, 
because  we  cannot  leave  the  body ;  but  continuity 
makes  it  not  unreasonable  to  suppose  that  they  present 
some  appearance  at  such  places.  Any  such  appearance 
would  be  included  among  sensibilia.  If — for  impossibile 
— there  were  a  complete  human  body  with  no  mind  in- 
side it,  all  those  sensibilia  would  exist,  in  relation  to  that 
body,  which  would  be  sense-data  if  there  were  a  mind  in 
the  body.  What  the  mind  adds  to  sensibilia,  in  fact,  is 
merely  awareness  :  everything  else  is  physical  or  physio- 
logical. 

IV.   SENSE-DATA  ARE  PHYSICAL 

Before  discussing  this  question  it  will  be  well  to  define 
the  sense  in  which  the  terms  "  mental  "  and  "  physical  " 
are  to  be  used.  The  word  "  physical,"  in  all  preliminary 
discussions,  is  to  be  understood  as  meaning  "  what  is 
dealt  with  by  physics."  Physics,  it  is  plain,  tells  us  some- 
thing about  some  of  the  constituents  of  the  actual  world  ; 
what  these  constituents  are  may  be  doubtful,  but  it  is 
they  that  are  to  be  called  physical,  whatever  their  nature 
may  prove  to  be. 

The  definition  of  the  term  "  mental  "  is  more  difficult, 
and  can  only  be  satisfactorily  given  after  many  difficult 
controversies  have  been  discussed  and  decided.  For 
present  purposes  therefore  I  must  content  myself  with 
assuming  a  dogmatic  answer  to  these  controversies.  I 
shall  call  a  particular  "  mental "  when  it  is  aware  of 
something,  and  I  shall  call  a  fact  "  mental  "  when  it 
contains  a  mental  particular  as  a  constituent. 


SENSE-DATA   AND   PHYSICS  151 

It  will  be  seen  that  the  mental  and  the  physical  are  not 
necessarily  mutually  exclusive,  although  I  know  of  no 
reason  to  suppose  that  they  overlap. 

The  doubt  as  to  the  correctness  of  our  definition  of  the 
"  mental "  is  of  little  importance  in  our  present  dis- 
cussion. For  what  I  am  concerned  to  maintain  is  that 
sense-data  are  physical,  and  this  being  granted  it  is  a 
matter  of  indifference  in  our  present  inquiry  whether  or 
not  they  are  also  mental.  Although  I  do  not  hold,  with 
Mach  and  James  and  the  "new  realists,"  that  the 
difference  between  the  mental  and  the  physical  is  merely 
one  of  arrangement,  yet  what  I  have  to  say  in  the  present 
paper  is  compatible  with  their  doctrine  and  might  have 
been  reached  from  their  standpoint. 

In  discussions  on  sense-data,  two  questions  are  com- 
monly confused,  namely  : 

(i)  Do  sensible  objects  persist  when  we  are  not  sensible 
of  them  ?  in  other  words,  do  sensibilia  which  are  data  at  a 
certain  time  sometimes  continue  to  exist  at  timeswhenthey 
are  not  data  ?  And  (2)  are  sense-data  mental  or  physical  ? 

I  propose  to  assert  that  sense-data  are  physical,  while 
yet  maintaining  that  they  probably  never  persist  un- 
changed after  ceasing  to  be  data.  The  view  that  they  do 
not  persist  is  often  thought,  quite  erroneously  in  my 
opinion,  to  imply  that  they  are  mental ;  and  this  has,  I 
believe,  been  a  potent  source  of  confusion  in  regard  to 
our  present  problem.  If  there  were,  as  some  have  held, 
a  logical  impossibility  in  sense-data  persisting  after  ceasing 
to  be  data,  that  certainly  would  tend  to  show  that  they 
were  mental ;  but  if,  as  I  contend,  their  non-persistence 
is  merely  a  probable  inference  from  empirically  ascer- 
tained causal  laws,  then  it  carries  no  such  implication 
with  it,  and  we  are  quite  free  to  treat  them  as  part  of  the 
subject-matter  of  physics. 


MYSTICISM   AND   LOGIC 

Logically  a  sense-datum  is  an  object,  a  particular  of 
which  the  subject  is  aware.  It  does  not  contain  the 
subject  as  a  part,  as  for  example  beliefs  and  volitions  do. 
The  existence  of  the  sense-datum  is  therefore  not  logically 
dependent  upon  that  of  the  subject ;  for  the  only  way, 
so  far  as  I  know,  in  which  the  existence  of  A  can  be 
logically  dependent  upon  the  existence  of  B  is  when  B 
is  part  of  A.  There  is  therefore  no  a  priori  reason  why  a 
particular  which  is  a  sense-datum  should  not  persist 
after  it  has  ceased  to  be  a  datum,  nor  why  other  similar 
particulars  should  not  exist  without  ever  being  data. 
The  view  that  sense-data  are  mental  is  derived,  no  doubt, 
in  part  from  their  physiological  subjectivity,  but  in  part 
also  from  a  failure  to  distinguish  between  sense-data  and 
"  sensations."  By  a  sensation  I  mean  the  fact  consisting 
in  the  subject's  awareness  of  the  sense-datum.  Thus  a 
sensation  is  a  complex  of  which  the  subject  is  a  con- 
stituent and  which  therefore  is  mental.  The  sense-datum, 
on  the  other  hand,  stands  over  against  the  subject  as  that 
external  object  of  which  in  sensation  the  subject  is 
aware.  It  is  true  that  the  sense-datum  is  in  many  cases 
in  the  subject's  body,  but  the  subject's  body  is  as  dis- 
tinct from  the  subject  as  tables  and  chairs  are,  and  is  in 
fact  merely  a  part  of  the  material  world.  So  soon,  there- 
fore, as  sense-data  are  clearly  distinguished  from  sensa- 
tions, and  as  their  subjectivity  is  recognised  to  be  physio- 
logical not  psychical,  the  chief  obstacles  in  the  way  of 
regarding  them  as  physical  are  removed. 


V.        SENSIBILIA       AND       THINGS 

But  if  "  sensibilia  "  are  to  be  recognised  as  the  ultimate 
constituents  of  the  physical  world,  a  long  and  difficult 
journey  is  to  be  performed  before  we  can  arrive  either  at 


SENSE-DATA  AND   PHYSICS  153 

the  "  thing  "  of  common  sense  or  at  the  "matter  "  of 
physics.  The  supposed  impossibility  of  combining  the 
different  sense-data  which  are  regarded  as  appearances  of 
the  same  "  thing  "  to  different  people  has  made  it  seem 
as  though  these  "  sensibilia  "  must  be  regarded  as  mere 
subjective  phantasms.  A  given  table  will  present  to  one 
man  a  rectangular  appearance,  while  to  another  it  appears 
to  have  two  acute  angles  and  two  obtuse  angles  ;  to  one 
man  it  appears  brown,  while  to  another,  towards  whom 
it  reflects  the  light,  it  appears  white  and  shiny.  It  is 
said,  not  wholly  without  plausibility,  that  these  different 
shapes  and  different  colours  cannot  co-exist  simul- 
taneously in  the  same  place,  and  cannot  therefore  both 
be  constituents  of  the  physical  world.  This  argument  I 
must  confess  appeared  to  me  until  recently  to  be  irre- 
futable. The  contrary  opinion  has,  however,  been  ably 
maintained  by  Dr.  T.  P.  Nunn  in  an  article  entitled  :  "Are 
Secondary  Qualities  Independent  of  Perception  ?  "l  The 
supposed  impossibility  derives  its  apparent  force  from  the 
phrase  :  "in  the  same  place,"  and  it  is  precisely  in  this 
phrase  that  its  weakness  lies.  The  conception  of  space 
is  too  often  treated  in  philosophy — even  by  those  who  on 
reflection  would  not  defend  such  treatment — as  though  it 
were  as  given,  simple,  and  unambiguous  as  Kant,  in  his 
psychological  innocence,  supposed.  It  is  the  un perceived 
ambiguity  of  the  word  "  place  "  which,  as  we  shall  shortly 
see,  has  caused  the  difficulties  to  realists  and  given  an  un- 
deserved advantage  to  their  opponents.  Two  "  places  " 
of  different  kinds  are  involved  in  every  sense-datum, 
namely  the  place  at  which  it  appears  and  the  place  from 
which  it  appears.  These  belong  to  different  spaces, 
although,  as  we  shall  see,  it  is  possible,  with  certain 
limitations,  to  establish  a  correlation  between  them. 

1  Proc.  Arisf.  Soc.,  1909-1910,  pp.  191-218. 


'54 

What  we  call  the  different  appearances  of  the  same  thing 
to  different  observers  are  each  in  a  space  private  to  the 
observer  concerned.  No  place  in  the  private  world  of 
one  observer  is  identical  with  a  place  in  the  private  world 
of  another  observer.  There  is  therefore  no  question  of 
combining  the  different  appearances  in  the  one  place  ; 
and  the  fact  that  they  cannot  all  exist  in  one  place  affords 
accordingly  no  ground  whatever  for  questioning  their 
physical  reality.  The  "  thing  "  of  common  sense  may  in 
fact  be  identified  with  the  whole  class  of  its  appearances 
— where,  however,  we  must  include  among  appearances 
not  only  those  which  are  actual  sense-data,  but  also 
those  "  sensibilia,"  if  any,  which,  on  grounds  of  con- 
tinuity and  resemblance,  are  to  be  regarded  as  belonging 
to  the  same  system  of  appearances,  although  there 
happen  to  be  no  observers  to  whom  they  are  data. 

An  example  may  make  this  clearer.  Suppose  there  are 
a  number  of  people  in  a  room,  all  seeing,  as  they  say,  the 
same  tables  and  chairs,  walls  and  pictures.  No  two  of 
these  people  have  exactly  the  same  sense-data,  yet  there 
is  sufficient  similarity  among  their  data  to  enable  them 
to  group  together  certain  of  these  data  as  appearances  of 
one  "  thing  "  to  the  several  spectators,  and  others  as 
appearances  of  another  "  thing."  Besides  the  appear- 
ances which  a  given  thing  in  the  room  presents  to  the 
actual  spectators,  there  are,  we  may  suppose,  other 
appearances  which  it  would  present  to  other  possible 
spectators.  If  a  man  were  to  sit  down  between  two 
others,  the  appearance  which  the  room  would  present  to 
him  would  be  intermediate  between  the  appearances 
which  it  presents  to  the  two  others  :  and  although  this 
appearance  would  not  exist  as  it  is  without  the  sense 
organs,  nerves  and  brain,  of  the  newly  arrived  spectator, 
still  it  is  not  unnatural  to  suppose  that,  from  the  position 


SENSE-DATA   AND   PHYSICS  155 

which  he  now  occupies,  some  appearance  of  the  room 
existed  before  his  arrival.  This  supposition,  however, 
need  merely  be  noticed  and  not  insisted  upon. 

Since  the  "  thing  "  cannot,  without  indefensible  par- 
tiality, be  identified  with  any  single  one  of  its  appear- 
ances, it  came  to  be  thought  of  as  something  distinct 
from  all  of  them  and  underlying  them.  But  by  the  prin- 
ciple of  Occam's  razor,  if  the  class  of  appearances  will 
fulfil  the  purposes  for  the  sake  of  which  the  thing  was 
invented  by  the  prehistoric  metaphysicians  to  whom 
common  sense  is  due,  economy  demands  that  we  should 
identify  the  thing  with  the  class  of  its  appearances.  It  is 
not  necessary  to  deny  a  substance  or  substratum  underly- 
ing these  appearances  ;  it  is  merely  expedient  to  abstain 
from  asserting  this  unnecessary  entity.  Our  procedure 
here  is  precisely  analogous  to  that  which  has  swept  away 
from  the  philosophy  of  mathematics  the  useless  menagerie 
of  metaphysical  monsters  with  which  it  used  to  be  in- 
fested. 

VI.  CONSTRUCTIONS  VERSUS  INFERENCES 

Before  proceeding  to  analyse  and  explain  the  am- 
biguities of  the  word  "  place,"  a  few  general  remarks  on 
method  are  desirable.  The  supreme  maxim  in  scientific 
philosophising  is  this  : 

Wherever  possible,  logical  constructions  are  to  be  sub- 
stituted for  inferred  entities. 

Some  examples  of  the  substitution  of  construction  for 
inference  in  the  realm  of  mathematical  philosophy  may 
serve  to  elucidate  the  uses  of  this  maxim.  Take  first  the 
case  of  irrationals.  In  old  days,  irrationals  were  inferred 
as  the  supposed  limits  of  series  of  rationals  which  had  no 
rational  limit  ;  but  the  objection  to  this  procedure  was 


156  MYSTICISM   AND   LOGIC 

that  it  left  the  existence  of  irrationals  merely  optative, 
and  for  this  reason  the  stricter  methods  of  the  present 
day  no  longer  tolerate  such  a  definition.  We  now  define 
an  irrational  number  as  a  certain  class  of  ratios,  thus 
constructing  it  logically  by  means  of  ratios,  instead  of 
arriving  at  it  by  a  doubtful  inference  from  them.  Take 
again  the  case  of  cardinal  numbers.  Two  equally 
numerous  collections  appear  to  have  something  in 
common  :  this  something  is  supposed  to  be  their  car- 
dinal number.  But  so  long  as  the  cardinal  number  is 
inferred  from  the  collections,  not  constructed  in  terms 
of  them,  its  existence  must  remain  in  doubt,  unless  in 
virtue  of  a  metaphysical  postulate  ad  hoc.  By  defining 
the  cardinal  number  of  a  given  collection  as  the  class  of 
all  equally  numerous  collections,  we  avoid  the  necessity 
of  this  metaphysical  postulate,  and  thereby  remove  a 
needless  element  of  doubt  from  the  philosophy  of  arith- 
metic. A  similar  method,  as  I  have  shown  elsewhere, 
can  be  applied  to  classes  themselves,  which  need  not  be 
supposed  to  have  any  metaphysical  reality,  but  can  be 
regarded  as  symbolically  constructed  fictions. 

The  method  by  which  the  construction  proceeds  is 
closely  analogous  in  these  and  all  similar  cases.  Given  a 
set  of  propositions  nominally  dealing  with  the  supposed 
inferred  entities,  we  observe  the  properties  which  are 
required  of  the  supposed  entities  in  order  to  make  these 
propositions  true.  By  dint  of  a  little  logical  ingenuity, 
we  then  construct  some  logical  function  of  less  hypo- 
thetical entities  which  has  the  requisite  properties.  This 
constructed  function  we  substitute  for  the  supposed  in- 
ferred entities,  and  thereby  obtain  a  new  and  less  doubtful 
interpretation  of  the  body  of  propositions  in  question. 
This  method,  so  fruitful  in  the  philosophy  of  mathematics, 
will  be  found  equally  applicable  in  the  philosophy  of 


SENSE-DATA  AND   PHYSICS  157 

physics,  where,  I  do  not  doubt,  it  would  have  been  applied 
long  ago  but  for  the  fact  that  all  who  have  studied  this 
subject  hitherto  have  been  completely  ignorant  of  mathe- 
matical logic.  I  myself  cannot  claim  originality  in  the 
application  of  this  method  to  physics,  since  I  owe  the 
suggestion  and  the  stimulus  for  its  application  entirely 
to  my  friend  and  collaborator  Dr.  Whitehead,  who  is 
engaged  in  applying  it  to  the  more  mathematical  portions 
of  the  region  intermediate  between  sense-data  and  the 
points,  instants  and  particles  of  physics. 

A  complete  application  of  the  method  which  substitutes 
constructions  for  inferences  would  exhibit  matter  wholly 
in  terms  of  sense-data,  and  even,  we  may  add,  of  the  sense- 
data  of  a  single  person,  since  the  sense-data  of  others 
cannot  be  known  without  some  element  of  inference. 
This,  however,  must  remain  for  the  present  an  ideal,  to 
be  approached  as  nearly  as  possible,  but  to  be  reached,  if 
at  all,  only  after  a  long  preliminary  labour  of  which  as 
yet  we  can  only  see  the  very  beginning.  The  inferences 
which  are  unavoidable  can,  however,  be  subjected  to 
certain  guiding  principles.  In  the  first  place  they  shoiild 
always  be  made  perfectly  explicit,  and  should  be  formulated 
in  the  most  general  manner  possible.  In  the  second  place 
the  inferred  entities  should,  whenever  this  can  be  done,  be 
similar  to  those  whose  existence  is  given,  rather  than,  like 
the  Kantian  Ding  an  sich,  something  wholly  remote  from 
the  data  which  nominally  support  the  inference.  The 
inferred  entities  which  I  shall  allow  myself  are  of  two 
kinds  :  (a)  the  sense-data  of  other  people,  in  favour  of 
which  there  is  the  evidence  of  testimony,  resting  ulti- 
mately upon  the  analogical  argument  in  favour  of  minds 
other  than  my  own  ;  (&)  the  "  sensibilia  "  which  would 
appear  from  places  where  there  happen  to  be  no  minds, 
and  which  I  suppose  to  be  real  although  they  are  no  one's 


158  MYSTICISM   AND   LOGIC 

data.  Of  these  two  classes  of  inferred  entities,  the  first 
will  probably  be  allowed  to  pass  unchallenged.  It  would 
give  me  the  greatest  satisfaction  to  be  able  to  dispense 
with  it,  and  thus  establish  physics  upon  a  solipsistic 
basis  ;  but  those — and  I  fear  they  are  the  majority — in 
whom  the  human  affections  are  stronger  than  the  desire 
for  logical  economy,  will,  no  doubt,  not  share  my  desire 
to  render  solipsism  scientifically  satisfactory.  The  second 
class  of  inferred  entities  raises  much  more  serious  ques- 
tions. It  may  be  thought  monstrous  to  maintain  that  a 
thing  can  present  any  appearance  at  all  in  a  place  where 
no  sense  organs  and  nervous  structure  exist  through  which 
it  could  appear.  I  do  not  myself  feel  the  monstrosity  ; 
nevertheless  I  should  regard  these  supposed  appearances 
only  in  the  light  of  a  hypothetical  scaffolding,  to  be  used 
while  the  edifice  of  physics  is  being  raised,  though 
possibly  capable  of  being  removed  as  soon  as  the  edifice  is 
completed.  These  "  sensibilia  "  which  are  not  data  to 
anyone  are  therefore  to  be  taken  rather  as  an  illustrative 
hypothesis  and  as  an  aid  in  preliminary  statement  than 
as  a  dogmatic  part  of  the  philosophy  of  physics  in  its 
final  form. 

VII.      PRIVATE    SPACE    AND    THE    SPACE    OF 
PERSPECTIVES 

We  have  now  to  explain  the  ambiguity  in  the  word 
"  place,"  and  how  it  comes  that  two  places  of  different 
sorts  are  associated  with  every  sense-datum,  namely  the 
place  at  which  it  is  and  the  place  from  which  it  is  per- 
ceived. The  theory  to  be  advocated  is  closely  analogous 
to  Leibniz's  monadology,  from  which  it  differs  chiefly  in 
being  less  smooth  and  tidy. 

The  first  fact  to  notice  is  that,  so  far  as  can  be  dis- 
covered, no  sensibile  is  ever  a  datum  to  two  people  at 


SENSE-DATA  AND   PHYSICS  159 

once.  The  things  seen  by  two  different  people  are  often 
closely  similar,  so  similar  that  the  same  words  can  be  used 
to  denote  them,  without  which  communication  with 
others  concerning  sensible  objects  would  be  impossible. 
But,  in  spite  of  this  similarity,  it  would  seem  that  some 
difference  always  arises  from  difference  in  the  point  of 
view.  Thus  each  person,  so  far  as  his  sense-data  are  con- 
cerned, lives  in  a  private  world.  This  private  world 
contains  its  own  space,  or  rather  spaces,  for  it  would 
seem  that  only  experience  teaches  us  to  correlate  the 
space  of  sight  with  the  space  of  touch  and  with  the 
various  other  spaces  of  other  senses.  This  multiplicity 
of  private  spaces,  however,  though  interesting  to  the 
psychologist,  is  of  no  great  importance  in  regard  to  our 
present  problem,  since  a  merely  solipsistic  experience 
enables  us  to  correlate  them  into  the  one  private  space 
which  embraces  all  our  own  sense-data.  The  place  at 
which  a  sense-datum  is,  is  a  place  in  private  space.  This 
place  therefore  is  different  from  any  place  in  the  private 
space  of  another  percipient.  For  if  we  assume,  as  logical 
economy  demands,  that  all  position  is  relative,  a  place  is 
only  definable  by  the  things  in  or  around  it,  and  therefore 
the  same  place  cannot  occur  in  two  private  worlds  which 
have  no  common  constituent.  The  question,  therefore, 
of  combining  what  we  call  different  appearances  of  the 
same  thing  in  the  same  place  does  not  arise,  and  the  fact 
that  a  given  object  appears  to  different  spectators  to 
have  different  shapes  and  colours  affords  no  argument 
against  the  physical  reality  of  all  these  shapes  and 
colours. 

In  addition  to  the  private  spaces  belonging  to  the 
private  worlds  of  different  percipients,  there  is,  however, 
another  space,  in  which  one  whole  private  world  counts 
as  a  point,  or  at  least  as  a  spatial  unit.  This  might  be 


i6o  MYSTICISM   AND   LOGIC 

described  as  the  space  of  points  of  view,  since  each 
private  world  may  be  regarded  as  the  appearance 
which  the  universe  presents  from  a  certain  point  of 
view.  I  prefer,  however,  to  speak  of  it  as  the  space  of 
perspectives,  in  order  to  obviate  the  suggestion  that  a 
private  world  is  only  real  when  someone  views  it. 
And  for  the  same  reason,  when  I  wish  to  speak  of  a 
private  world  without  assuming  a  percipient,  I  shall  call 
it  a  "  perspective." 

We  have  now  to  explain  how  the  different  perspectives 
are  ordered  in  one  space.  This  is  effected  by  means  of  the 
correlated  "  sensibilia  "  which  are  regarded  as  the  appear- 
ances, in  different  perspectives,  of  one  and  the  same  thing. 
By  moving,  and  by  testimony,  we  discover  that  two 
different  perspectives,  though  they  cannot  both  contain 
the  same  "sensibilia,"  may  nevertheless  contain  very 
similar  ones  ;  and  the  spatial  order  of  a  certain  group  of 
"  sensibilia  "  in  a  private  space  of  one  perspective  is 
found  to  be  identical  with,  or  very  similar  to,  the  spatial 
order  of  the  correlated  "  sensibilia  "  in  the  private  space 
of  another  perspective.  In  this  way  one  "  sensibile  "  in 
one  perspective  is  correlated  with  one  "  sensibile  "  in 
another.  Such  correlated  "  sensibilia  "  will  be  called 
"  appearances  of  one  thing."  In  Leibniz's  monadology, 
since  each  monad  mirrored  the  whole  universe,  there  was 
in  each  perspective  a  "  sensibile  "  which  was  an  appear- 
ance of  each  thing.  In  our  system  of  perspectives,  we 
make  no  such  assumption  of  completeness.  A  given 
thing  will  have  appearances  in  some  perspectives,  but 
presumably  not  in  certain  others.  The  "  thing  "  being 
denned  as  the  class  of  its  appearances,  if  K  is  the  class  of 
perspectives  in  which  a  certain  thing  0  appears,  then  0  is 
a  member  of  the  multiplicative  class  of  K  ,  K  being  a  class 
of  mutually  exclusive  classes  of  "  sensibilia."  And 


SENSE-DATA   AND   PHYSICS  161 

similarly  a  perspective  is  a  member  of  the  multiplicative 
class  of  the  things  which  appear  in  it. 

The  arrangement  of  perspectives  in  a  space  is  effected 
by  means  of  the  differences  between  the  appearances  of  a 
given  thing  in  the  various  perspectives.  Suppose,  say, 
that  a  certain  penny  appears  in  a  number  of  different 
perspectives  ;  in  some  it  looks  larger  and  in  some  smaller, 
in  some  it  looks  circular,  in  others  it  presents  the  appear- 
ance of  an  ellipse  of  varying  eccentricity.  We  may  collect 
together  all  those  perspectives  in  which  the  appearance  of 
the  penny  is  circular.  These  we  will  place  on  one  straight 
line,  ordering  them  in  a  series  by  the  variations  in  the 
apparent  size  of  the  penny.  Those  perspectives  in  which 
the  penny  appears  as  a  straight  line  of  a  certain  thickness 
will  similarly  be  placed  upon  a  plane  (though  in  this  case 
there  will  be  many  different  perspectives  in  which  the 
penny  is  of  the  same  size ;  when  one  arrangement  is  com- 
pleted these  will  form  a  circle  concentric  with  the  penny), 
and  ordered  as  before  by  the  apparent  size  of  the  penny. 
By  such  means,  all  those  perspectives  in  which  the  penny 
presents  a  visual  appearance  can  be  arranged  in  a  three- 
dimensional  spatial  order.  Experience  shows  that  the  same 
spatial  order  of  perspectives  would  have  resulted  if,  instead 
of  the  penny,  we  had  chosen  any  other  thing  which 
appeared  in  all  the  perspectives  in  question,  or  any  other 
method  of  utilising  the  differences  between  the  appearances 
of  the  same  things  in  different  perspectives.  It  is  this 
empirical  fact  which  has  made  it  possible  to  construct 
the  one  all-embracing  space  of  physics. 

The  space  whose  construction  has  just  been  explained, 
and  whose  elements  are  whole  perspectives,  will  be  called 
"  perspective-space." 


M 


162  MYSTICISM   AND   LOGIC 

VIII.   THE  PLACING  OF  "  THINGS  "  AND   "  SENSIBILIA  "   IN 
PERSPECTIVE   SPACE 

The  world  which  we  have  so  far  constructed  is  a  world 
of  six  dimensions,  since  it  is  a  three-dimensional  series  of 
perspectives,  each  of  which  is  itself  three-dimensional. 
We  have  now  to  explain  the  correlation  between  the  per- 
spective space  and  the  various  private  spaces  contained 
within  the  various  perspectives  severally.  It  is  by  means 
of  this  correlation  that  the  one  three-dimensional  space 
of  physics  is  constructed  ;  and  it  is  because  of  the  un- 
conscious performance  of  this  correlation  that  the  dis- 
tinction between  perspective  space  and  the  percipient's 
private  space  has  been  blurred,  with  disastrous  results 
for  the  philosophy  of  physics.  Let  us  revert  to  our 
penny  :  the  perspectives  in  which  the  penny  appears 
larger  are  regarded  as  being  nearer  to  the  penny  than 
those  in  which  it  appears  smaller,  but  as  far  as  experience 
goes  the  apparent  size  of  the  penny  will  not  grow  beyond 
a  certain  limit,  namely,  that  where  (as  we  say)  the  penny 
is  so  near  the  eye  that  if  it  were  any  nearer  it  could  not 
be  seen.  By  touch  we  may  prolong  the  series  until  the 
penny  touches  the  eye,  but  no  further.  If  we  have  been 
travelling  along  a  line  of  perspectives  in  the  previously 
denned  sense,  we  may,  however,  by  imagining  the  penny 
removed,  prolong  the  line  of  perspectives  by  means,  say, 
of  another  penny  ;  and  the  same  may  be  done  with  any 
other  line  of  perspectives  denned  by  means  of  the  penny. 
All  these  lines  meet  in  a  certain  place,  that  is,  in  a  certain 
perspective.  This  perspective  will  be  defined  as  "  the 
place  where  the  penny  is." 

It  is  now  evident  in  what  sense  two  places  in  con- 
structed physical  space  are  associated  with  a  given 
"sensibile."  There  is  first  the  place  which  is  the  per- 


SENSE-DATA   AND   PHYSICS  163 

spective  of  which  the  "  sensibile  "  is  a  member.  This  is 
the  place  from  which  the  "  sensibile  "  appears.  Secondly 
there  is  the  place  where  the  thing  is  of  which  the  "  sen- 
sibile "  is  a  member,  in  other  words  an  appearance  ;  this 
is  the  place  at  which  the  "  sensibile  "  appears.  The 
"sensibile"  which  is  a  member  of  one  perspective  is 
correlated  with  another  perspective,  namely,  that  which 
is"  the  place  where  the  thing  is  of  which  the  "  sensibile  " 
is  an  appearance.  To  the  psychologist  the  "  place  from 
which"  is  the  more  interesting,  and  the  "sensibile" 
accordingly  appears  to  him  subjective  and  where  the 
percipient  is.  To  the  physicist  the  "  place  at  which  "  is 
the  more  interesting,  and  the  "sensibile"  accordingly 
appears  to  him  physical  and  external.  The  causes,  limits 
and  partial  justification  of  each  of  these  two  apparently 
incompatible  views  are  evident  from  the  above  duplicity 
of  places  associated  with  a  given  "  sensibile." 

We  have  seen  that  we  can  assign  to  a  physical  thing  a 
place  in  the  perspective  space.  In  this  way  different 
parts  of  our  body  acquire  positions  in  perspective  space, 
and  therefore  there  is  a  meaning  (whether  true  or  false 
need  not  much  concern  us)  in  saying  that  the  perspective 
to  which  our  sense-data  belong  is  inside  our  head.  Since 
our  mind  is  correlated  with  the  perspective  to  which  our 
sense-data  belong,  we  may  regard  this  perspective  as 
being  the  position  of  our  mind  in  perspective  space.  If, 
therefore,  this  perspective  is,  in  the  above  defined  sense, 
inside  our  head,  there  is  a  good  meaning  for  the  state- 
ment that  the  mind  is  in  the  head.  We  can  now  say  of 
the  various  appearances  of  a  given  thing  that  some  of 
them  are  nearer  to  the  thing  than  others ;  those  are 
nearer  which  belong  to  perspectives  that  are  nearer  to 
"  the  place  where  the  thing  is."  We  can  thus  find  a 
meaning,  true  or  false,  for  the  statement  that  more  is  to 


164  MYSTICISM   AND   LOGIC 

be  learnt  about  a  thing  by  examining  it  close  to  than  by 
viewing  it  from  a  distance.  We  can  also  find  a  meaning 
for  the  phrase  "  the  things  which  intervene  between  the 
subject  and  a  thing  of  which  an  appearance  is  a  datum 
to  him."  One  reason  often  alleged  for  the  subjectivity 
of  sense-data  is  that  the  appearance  of  a  thing  may  change 
when  we  find  it  hard  to  suppose  that  the  thing  itself  has 
changed — for  example,  when  the  change  is  due  to  our 
shutting  our  eyes,  or  to  our  screwing  them  up  so  as  to 
make  the  thing  look  double.  If  the  thing  is  defined  as 
the  class  of  its  appearances  (which  is  the  definition  adopted 
above),  there  is  of  course  necessarily  some  change  in  the 
thing  whenever  any  one  of  its  appearances  changes. 
Nevertheless  there  is  a  very  important  distinction  between 
two  different  ways  in  which  the  appearances  may  change. 
If  after  looking  at  a  thing  I  shut  my  eyes,  the  appearance 
of  my  eyes  changes  in  every  perspective  in  which  there 
is  such  an  appearance,  whereas  most  of  the  appearances 
of  the  thing  will  remain  unchanged.  We  may  say,  as  a 
matter  of  definition,  that  a  thing  changes  when,  however 
near  to  the  thing  an  appearance  of  it  may  be,  there  are 
changes  in  appearances  as  near  as,  or  still  nearer  to,  the 
thing.  On  the  other  hand  we  shall  say  that  the  change  is 
in  some  other  thing  if  all  appearances  of  the  thing  which 
are  at  not  more  than  a  certain  distance  from  the  thing 
remain  unchanged,  while  only  comparatively  distant 
appearances  of  the  thing  are  altered.  From  this  con- 
sideration we  are  naturally  led  to  the  consideration  of 
matter,  which  must  be  our  next  topic. 

IX.   THE  DEFINITION  OF  MATTER 

We  defined  the  "  physical  thing  "  as  the  class  of  its 
appearances,  but  this  can  hardly  be  taken  as  a  definition 
of  matter.  We  want  to  be  able  to  express  the  fact  that 


SENSE-DATA  AND   PHYSICS  165 

the  appearance  of  a  thing  in  a  given  perspective  is 
causally  affected  by  the  matter  between  the  thing  and  the 
perspective.  We  have  found  a  meaning  for  "  between  a 
thing  and  a  perspective."  But  we  want  matter  to  be 
something  other  than  the  whole  class  of  appearances  of  a 
thing,  in  order  to  state  the  influence  of  matter  on  appear- 
ances. 

We  commonly  assume  that  the  information  we  get 
about  a  thing  is  more  accurate  when  the  thing  is  nearer. 
Far  off,  we  see  it  is  a  man  ;  then  we  see  it  is  Jones  ;  then 
we  see  he  is  smiling.  Complete  accuracy  would  only  be 
attainable  as  a  limit  :  if  the  appearances  of  Jones  as  we 
approach  him  tend  towards  a  limit,  that  limit  may  be 
taken  to  be  what  Jones  really  is.  It  is  obvious  that  from 
the  point  of  view  of  physics  the  appearances  of  a  thing 
close  to  "  count  "  more  than  the  appearances  far  off.  We 
may  therefore  set  up  the  following  tentative  definition  : 

The  matter  of  a  given  thing  is  the  limit  of  its  appear- 
ances as  their  distance  from  the  thing  diminishes. 

It  seems  probable  that  there  is  something  in  this 
definition,  but  it  is  not  quite  satisfactory,  because  em- 
pirically there  is  no  such  limit  to  be  obtained  from  sense- 
data.  The  definition  will  have  to  be  eked  out  by  con- 
structions and  definitions.  But  probably  it  suggests  the 
right  direction  in  which  to  look. 

We  are  now  in  a  position  to  understand  in  outline  the 
reverse  journey  from  matter  to  sense-data  which  is  per- 
formed by  physics.  The  appearance  of  a  thing  in  a  given 
perspective  is  a  function  of  the  matter  composing  the 
thing  and  of  the  intervening  matter.  The  appearance  of 
a  thing  is  altered  by  intervening  smoke  or  mist,  by  blue 
spectacles  or  by  alterations  in  the  sense-organs  or  nerves 
of  the  percipient  (which  also  must  be  reckoned  as  part  of 
the  intervening  medium).  The  nearer  we  approach  to 


166  MYSTICISM   AND   LOGIC 

the  thing,  the  less  its  appearance  is  affected  by  the  inter- 
vening matter.  As  we  travel  further  and  further  from  the 
thing,  its  appearances  diverge  more  and  more  from  their 
initial  character  ;  and  the  causal  laws  of  their  divergence 
are  to  be  stated  in  terms  of  the  matter  which  lies  between 
them  and  the  thing.  Since  the  appearances  at  very  small 
distances  are  less  affected  by  causes  other  than  the  thing 
itself,  we  come  to  think  that  the  limit  towards  which  these 
appearances  tend  as  the  distance  diminishes  is  what  the 
thing  "  really  is,"  as  opposed  to  what  it  merely  seems  to 
be.  This,  together  with  its  necessity  for  the  statement  of 
causal  laws,  seems  to  be  the  source  of  the  entirely  erro- 
neous feeling  that  matter  is  more  "real"  than  sense- 
data. 

Consider  for  example  the  infinite  divisibility  of  matter. 
In  looking  at  a  given  thing  and  approaching  it,  one  sense- 
datum  will  become  several,  and  each  of  these  will  again 
divide.  Thus  one  appearance  may  represent  many  things, 
and  to  this  process  there  seems  no  end.  Hence  in  the 
limit,  when  we  approach  indefinitely  near  to  the  thing, 
there  will  be  an  indefinite  number  of  units  of  matter 
corresponding  to  what,  at  a  finite  distance,  is  only  one 
appearance.  This  is  how  infinite  divisibility  arises. 

The  whole  causal  efficacy  of  a  thing  resides  in  its  matter. 
This  is  in  some  sense  an  empirical  fact,  but  it  would  be  hard 
to  state  it  precisely,  because  "  causal  efficacy  "  is  difficult 
to  define. 

What  can  be  known  empirically  about  the  matter  of  a 
thing  is  only  approximate,  because  we  cannot  get  to  know 
the  appearances  of  the  thing  from  very  small  distances, 
and  cannot  accurately  infer  the  limit  of  these  appearances. 
But  it  is  inferred  approximately  by  means  of  the  appear- 
ances we  can  observe.  It  then  turns  out  that  these 
appearances  can  be  exhibited  by  physics  as  a  function  of 


SENSE-DATA   AND   PHYSICS  167 

the  matter  in  our  immediate  neighbourhood  ;  e.g.  the 
visual  appearance  of  a  distant  object  is  a  function  of  the 
light-waves  that  reach  the  eyes.  This  leads  to  confusions 
of  thought,  but  offers  no  real  difficulty. 

One  appearance,  of  a  visible  object  for  example,  is  not 
sufficient  to  determine  its  other  simultaneous  appearances, 
although  it  goes  a  certain  distance  towards  determining 
them.  The  determination  of  the  hidden  structure  of  a 
thing,  so  far  as  it  is  possible  at  all,  can  only  be  effected  by 
means  of  elaborate  dynamical  inferences. 

X.   TIME1 

It  seems  that  the  one  all-embracing  time  is  a  con- 
struction, like  the  one  all-embracing  space.  Physics 
itself  has  become  conscious  of  this  fact  through  the  dis- 
cussions connected  with  relativity. 

Between  two  perspectives  which  both  belong  to  one 
person's  experience,  there  will  be  a  direct  time-relation  of 
before  and  after.  This  suggests  a  way  of  dividing  history 
in  the  same  sort  of  way  as  it  is  divided  by  different 
experiences,  but  without  introducing  experience  or  any- 
thing mental :  we  may  define  a  "  biography  "  as  every- 
thing that  is  (directly)  earlier  or  later  than,  or  simul- 
taneous with,  a  given  "  sensibile."  This  will  give  a  series 
of  perspectives,  which  might  all  form  parts  of  one  person's 
experience,  though  it  is  not  necessary  that  all  or  any  of 
them  should  actually  do  so.  By  this  means,  the  history 
of  the  world  is  divided  into  a  number  of  mutually  exclusive 
biographies. 

1  On  this  subject,  compare  A  Theory  of  Time  and  Space,  by  Mr. 
A.  A.  Robb  (Camb.  Univ.  Press),  which  first  suggested  to  me  the  views 
advocated  here,  though  I  have,  for  present  purposes,  omitted  what  is 
most  interesting  and  novel  in  his  theory.  Mr.  Robb  has  given  a  sketch 
of  his  theory  in  a  pamphlet  with  the  same  title  (Heffer  and  Sons, 
Cambridge,  1913). 


168  MYSTICISM   AND   LOGIC 

We  have  now  to  correlate  the  times  in  the  different 
biographies.  The  natural  thing  would  be  to  say  that  the 
appearances  of  a  given  (momentary)  thing  in  two  different 
perspectives  belonging  to  different  biographies  are  to  be 
taken  as  simultaneous ;  but  this  is  not  convenient. 
Suppose  A  shouts  to  B,  and  B  replies  as  soon  as  he  hears 
A's  shout.  Then  between  A's  hearing  of  his  own  shout 
and  his  hearing  of  B's  there  is  an  interval ;  thus  if  we 
made  A's  and  B's  hearing  of  the  same  shout  exactly 
simultaneous  with  each  other,  we  should  have  events 
exactly  simultaneous  with  a  given  event  but  not  with 
each  other.  To  obviate  this,  we  assume  a  "  velocity  of 
sound."  That  is,  we  assume  that  the  time  when  B  hears 
A 's  shout  is  half-way  between  the  time  when  A  hears  his 
own  shout  and  the  time  when  he  hears  B's.  In  this  way 
the  correlation  is  effected. 

What  has  been  said  about  sound  applies  of  course 
equally  to  light.  The  general  principle  is  that  the 
appearances,  in  different  perspectives,  which  are  to  be 
grouped  together  as  constituting  what  a  certain  thing  is 
at  a  certain  moment,  are  not  to  be  all  regarded  as  being 
at  that  moment.  On  the  contrary  they  spread  outward 
from  the  thing  with  various  velocities  according  to  the 
nature  of  the  appearances.  Since  no  direct  means  exist 
of  correlating  the  time  in  one  biography  with  the  time  in 
another,  this  temporal  grouping  of  the  appearances 
belonging  to  a  given  thing  at  a  given  moment  is  in  part 
conventional.  Its  motive  is  partly  to  secure  the  verifica- 
tion of  such  maxims  as  that  events  which  are  exactly 
simultaneous  with  the  same  event  are  exactly  simul- 
taneous with  one  another,  partly  to  secure  convenience 
in  the  formulation  of  causal  laws. 


SENSE-DATA   AND   PHYSICS  169 

XI.   THE   PERSISTENCE   OF  THINGS   AND   MATTER 

Apart  from  any  of  the  fluctuating  hypotheses  of 
physics,  three  main  problems  arise  in  connecting  the 
world  of  physics  with  the  world  of  sense,  namely  : 

1.  the  construction  of  a  single  space  ; 

2.  the  construction  of  a  single  time  ; 

3.  the  construction  of  permanent  things  or  matter. 

We  have  already  considered  the  first  and  second  of 
these  problems  ;  it  remains  to  consider  the  third. 

We  have  seen  how  correlated  appearances  in  different 
perspectives  are  combined  to  form  one  "  thing  "  at  one 
moment  in  the  all-embracing  time  of  physics.  We  have 
now  to  consider  how  appearances  at  different  times  are 
combined  as  belonging  to  one  "  thing,"  and  how  we 
arrive  at  the  persistent  "  matter "  of  physics.  The 
assumption  of  permanent  substance,  which  technically 
underlies  the  procedure  of  physics,  cannot  of  course  be 
regarded  as  metaphysically  legitimate  :  just  as  the  one 
thing  simultaneously  seen  by  many  people  is  a  con- 
struction, so  the  one  thing  seen  at  different  times  by  the 
same  or  different  people  must  be  a  construction,  being  in 
fact  nothing  but  a  certain  grouping  of  certain  "  sensibilia." 

We  have  seen  that  the  momentary  state  of  a  "  thing  " 
is  an  assemblage  of  "  sensibilia,"  in  different  perspectives, 
not  all  simultaneous  in  the  one  constructed  time,  but 
spreading  out  from  "  the  place  where  the  thing  is  "  with 
velocities  depending  upon  the  nature  of  the  "  sensibilia." 
The  time  at  which  the  "  thing  "  is  in  this  state  is  the  lower 
limit  of  the  times  at  which  these  appearances  occur.  We 
have  now  to  consider  what  leads  us  to  speak  of  another 
set  of  appearances  as  belonging  to  the  same  "  thing  "  at 
a  different  time. 


170  MYSTICISM  AND   LOGIC 

For  this  purpose,  we  may,  at  least  to  begin  with, 
confine  ourselves  within  a  single  biography.  If  we  can 
always  say  when  two  "  sensibilia  "  in  a  given  biography 
are  appearances  of  one  thing,  then,  since  we  have  seen 
how  to  connect  "  sensibilia  "  in  different  biographies  as 
appearances  of  the  same  momentary  state  of  a  thing,  we 
shall  have  all  that  is  necessary  for  the  complete  con- 
struction of  the  history  of  a  thing. 

It  is  to  be  observed,  to  begin  with,  that  the  identity  of 
a  thing  for  common  sense  is  not  always  correlated  with 
the  identity  of  matter  for  physics.  A  human  body  is  one 
persisting  thing  for  common  sense,  but  for  physics  its 
matter  is  constantly  changing.  We  may  say,  broadly, 
that  the  common-sense  conception  is  based  upon  con- 
tinuity in  appearances  at  the  ordinary  distances  of  sense- 
data,  while  the  physical  conception  is  based  upon  the 
continuity  of  appearances  at  very  small  distances  from 
the  thing.  It  is  probable  that  the  common-sense  con- 
ception is  not  capable  of  complete  precision.  Let  us  there- 
fore concentrate  our  attention  upon  the  conception  of  the 
persistence  of  matter  in  physics. 

The  first  characteristic  of  two  appearances  of  the  same 
piece  of  matter  at  different  times  is  continuity.  The  two 
appearances  must  be  connected  by  a  series  of  inter- 
mediaries, which,  if  time  and  space  form  compact  series, 
must  themselves  form  a  compact  series.  The  colour  of 
the  leaves  is  different  in  autumn  from  what  it  is  in  summer; 
but  we  believe  that  the  change  occurs  gradually,  and  that, 
if  the  colours  are  different  at  two  given  times,  there  are 
intermediate  times  at  which  the  colours  are  intermediate 
between  those  at  the  given  times. 

But  there  are  two  considerations  that  are  important  as 
regards  continuity. 

First,  it  is  largely  hypothetical.    We  do  not  observe 


SENSE-DATA  AND   PHYSICS  171 

any  one  thing  continuously,  and  it  is  merely  a  hypo- 
thesis to  assume  that,  while  we  are  not  observing  it,  it 
passes  through  conditions  intermediate  between  those  in 
which  it  is  perceived.  During  uninterrupted  observa- 
tion, it  is  true,  continuity  is  nearly  verified  ;  but  even 
here,  when  motions  are  very  rapid,  as  in  the  case  of 
explosions,  the  continuity  is  not  actually  capable  of 
direct  verification.  Thus  we  can  only  say  that  the  sense- 
data  are  found  to  permit  a  hypothetical  complement  of 
"sensibilia  "  such  as  will  preserve  continuity,  and  that 
therefore  there  may  be  such  a  complement.  Since,  how- 
ever, we  have  already  made  such  use  of  hypothetical 
"  sensibilia,"  we  will  let  this  point  pass,  and  admit  such 
"  sensibilia,"  as  are  required  to  preserve  continuity. 

Secondly,  continuity  is  not  a  sufficient  criterion  of 
material  identity.  It  is  true  that  in  many  cases,  such  as 
rocks,  mountains,  tables,  chairs,  etc.,  where  the  appear- 
ances change  slowly,  continuity  is  sufficient,  but  in  other 
cases,  such  as  the  parts  of  an  approximately  homogeneous 
fluid,  it  fails  us  utterly.  We  can  travel  by  sensibly 
continuous  gradations  from  any  one  drop  of  the  sea  at 
any  one  time  to  any  other  drop  at  any  other  time.  We 
infer  the  motions  of  sea-water  from  the  effects  of  the 
current,  but  they  cannot  be  inferred  from  direct  sensible 
observation  together  with  the  assumption  of  continuity. 

The  characteristic  required  in  addition  to  continuity  is 
conformity  with  the  laws  of  dynamics.  Starting  from 
what  common  sense  regards  as  persistent  things,  and 
making  only  such  modifications  as  from  time  to  time 
seem  reasonable,  we  arrive  at  assemblages  of  "  sensibilia  " 
which  are  found  to  obey  certain  simple  laws,  namely  those 
of  dynamics.  By  regarding  "  sensibilia  "  at  different 
times  as  belonging  to  the  same  piece  of  matter,  we  are 
able  to  define  motion,  which  presupposes  the  assumption 


172  MYSTICISM  AND  LOGIC 

or  construction  of  something  persisting  throughout  the 
time  of  the  motion.  The  motions  which  are  regarded  as 
occurring,  during  a  period  in  which  all  the  "  sensibilia  " 
and  the  times  of  their  appearance  are  given,  will  be 
different  according  to  the  manner  in  which  we  combine 
"  sensibilia  "  at  different  times  as  belonging  to  the  same 
piece  of  matter.  Thus  even  when  the  whole  history  of 
the  world  is  given  in  every  particular,  the  question  what 
motions  take  place  is  still  to  a  certain  extent  arbitrary 
even  after  the  assumption  of  continuity.  Experience 
shows  that  it  is  possible  to  determine  motions  in  such  a 
way  as  to  satisfy  the  laws  of  dynamics,  and  that  this 
determination,  roughly  and  on  the  whole,  is  fairly  in 
agreement  with  the  common-sense  opinions  about  per- 
sistent things.  This  determination,  therefore,  is  adopted, 
and  leads  to  a  criterion  by  which  we  can  determine,  some- 
times practically,  sometimes  only  theoretically,  whether 
two  appearances  at  different  times  are  to  be  regarded  as 
belonging  to  the  same  piece  of  matter.  The  persistence 
of  all  matter  throughout  all  time  can,  I  imagine,  be 
secured  by  definition. 

To  recommend  this  conclusion,  we  must  consider  what 
it  is  that  is  proved  by  the  empirical  success  of  physics. 
What  is  proved  is  that  its  hypotheses,  though  unverifiablc 
where  they  go  beyond  sense-data,  are  at  no  point  in 
contradiction  with  sense-data,  but,  on  the  contrary,  are 
ideally  such  as  to  render  all  sense-data  calculable  when  a 
sufficient  collection  of  "  sensibilia "  is  given.  Now 
physics  has  found  it  empirically  possible  to  collect  sense- 
data  into  series,  each  series  being  regarded  as  belonging 
to  one  "  thing,"  and  behaving,  with  regard  to  the  laws 
of  physics,  in  a  way  in  which  series  not  belonging  to  one 
thing  would  in  general  not  behave.  If  it  is  to  be  un- 
ambiguous whether  two  appearances  belong  to  the  same 


SENSE-DATA   AND   PHYSICS  173 

thing  or  not,  there  must  be  only  one  way  of  grouping 
appearances  so  that  the  resulting  things  obey  the  laws  of 
physics.  It  would  be  very  difficult  to  prove  that  this  is 
the  case,  but  for  our  present  purposes  we  may  let  this 
point  pass,  and  assume  that  there  is  only  one  way.  Thus 
we  may  lay  down  the  following  definition  :  Physical 
things  are  those  series  of  appearances  whose  matter  obeys 
the  laws  of  physics.  That  such  series  exist  is  an  empirical 
fact,  which  constitutes  the  verifiability  of  physics. 

XII.   ILLUSIONS,   HALLUCINATIONS,   AND   DREAMS 

It  remains  to  ask  how,  in  our  system,  we  are  to  find  a 
place  for  sense-data  which  apparently  fail  to  have  the 
usual  connection  with  the  world  of  physics.  Such  sense- 
data  are  of  various  kinds,  requiring  somewhat  different 
treatment.  But  all  are  of  the  sort  that  would  be  called 
"  unreal,"  and  therefore,  before  embarking  upon  the  dis- 
cussion, certain  logical  remarks  must  be  made  upon  the 
conceptions  of  reality  and  unreality. 

Mr.  A.  Wolf1  says  : 

"  The  conception  of  mind  as  a  system  of  transparent 
activities  is,  I  think,  also  untenable  because  of  its  failure 
to  account  for  the  very  possibility  of  dreams  and  hallu- 
cinations. It  seems  impossible  to  realise  how  a  bare, 
transparent  activity  can  be  directed  to  what  is  not  there, 
to  apprehend  what  is  not  given." 

This  statement  is  one  which,  probably,  most  people 
would  endorse.    But  it  is  open  to  two  objections.    First 
it  is  difficult  to  see  how  an  activity,  however  un-  "  trans- 
parent," can  be  directed  towards  a  nothing  :  a  term  of  a 
relation  cannot  be  a  mere  nonentity.    Secondly,  no  reason 

1  "  Natural  Realism  and  Present  Tendencies  in  Philosophy,"  Proc. 
Arist.  Soc.,  1908-1909,  p.  165. 


174  MYSTICISM   AND   LOGIC 

is  given,  and  I  am  convinced  that  none  can  be  given,  for 
the  assertion  that  dream-objects  are  not  "  there  "  and 
not  "  given."  Let  us  take  the  second  point  first. 

(1)  The  belief  that  dream-objects  are  not  given  comes, 
I  think,  from  failure  to  distinguish,  as  regards  waking 
life,   between  the  sense-datum  and  the  corresponding 
"  thing."     In  dreams,  there  is  no  such  corresponding 
"  thing  "  as  the  dreamer  supposes ;    if,  therefore,  the 
"thing"  were  given  in  waking  life,  as  e.g.  Meinong 
maintains,1  then  there  would  be  a  difference  in  respect  of 
givenness  between  dreams  and  waking  life.    But  if,  as 
we  have  maintained,  what  is  given  is  never  the  thing,  but 
merely  one  of  the  "  sensibilia  "  which  compose  the  thing, 
then  what  we  apprehend  in  a  dream  is  just  as  much  given 
as  what  we  apprehend  in  waking  life. 

Exactly  the  same  argument  applies  as  to  the  dream- 
objects  being  "  there."  They  have  their  position  in  the 
private  space  of  the  perspective  of  the  dreamer ;  where 
they  fail  is  in  their  correlation  with  other  private  spaces 
and  therefore  with  perspective  space.  But  in  the  only 
sense  in  which  "  there  "  can  be  a  datum,  they  are  "  there  " 
just  as  truly  as  any  of  the  sense-data  of  waking  life. 

(2)  The  conception  of  "  illusion  "or  "  unreality,"  and 
the  correlative  conception  of  "reality,"  are  generally 
used  in  a  way  which  embodies  profound  logical  con- 
fusions.    Words  that  go  in  pairs,  such  as  "  real "  and 
"unreal,"    "existent"   and    "non-existent,"    "valid" 
and  "invalid,"  etc.,  are  all  derived  from  the  one  funda- 
mental pair,  "true"  and  "false."     Now  "true"  and 
"  false  "  are  applicable  only — except  in  derivative  signifi- 
cations—to propositions.    Thus  wherever  the  above  pairs 
can  be  significantly  applied,  we  must  be  dealing  either 
with  propositions  or  with  such  incomplete  phrases  as 

1  Die  Erfahrungsgrundlagen  unseres  Wissens,  p.  28. 


SENSE-DATA  AND   PHYSICS  175 

only  acquire  meaning  when  put  into  a  context  which, 
with  them,  forms  a  proposition.  Thus  such  pairs  of  words 
can  be  applied  to  descriptions*  but  not  to  proper  names  : 
in  other  words,  they  have  no  application  whatever  to 
data,  but  only  to  entities  or  non-entities  described  in 
terms  of  data. 

Let  us  illustrate  by  the  terms  "  existence  "  and  "  non- 
existence."  Given  any  datum  x,  it  is  meaningless  either 
to  assert  or  to  deny  that  x  "  exists."  We  might  be 
tempted  to  say  :  "Of  course  x  exists,  for  otherwise  it 
could  not  be  a  datum."  But  such  a  statement  is  really 
meaningless,  although  it  is  significant  and  true  to  say 
"My  present  sense-datum  exists,"  and  it  may  also  be 
true  that  "  x  is  my  present  sense-datum."  The  inference 
from  these  two  propositions  to  "  x  exists  "  is  one  which 
seems  irresistible  to  people  unaccustomed  to  logic  ;  yet 
the  apparent  proposition  inferred  is  not  merely  false,  but 
strictly  meaningless.  To  say  "  My  present  sense-datum 
exists  "  is  to  say  (roughly) :  "  There  is  an  object  of  which 
'my  present  sense-datum'  is  a  description."  But  we 
cannot  say  :  "  There  is  an  object  of  which  '  x '  is  a 
description,"  because  '  x  '  is  (in  the  case  we  are  supposing) 
a  name,  not  a  description.  Dr.  Whitehead  and  I  have 
explained  this  point  fully  elsewhere  (loc.  cit.)  with  the 
help  of  symbols,  without  which  it  is  hard  to  understand  ; 
I  shall  not  therefore  here  repeat  the  demonstration  of  the 
above  propositions,  but  shall  proceed  with  their  applica- 
tion to  our  present  problem. 

The  fact  that  "existence"  is  only  applicable  to 
descriptions  is  concealed  by  the  use  of  what  are  gram- 
matically proper  names  in  a  way  which  really  transforms 
them  into  descriptions.  It  is,  for  example,  a  legitimate 

1  Cf.  Principia  Mathematica,  Vol.  I,  *  14,  and  Introduction,  Chap. 
III.  For  the  definition  of  existence,  cf.  *  14.  02. 


176  MYSTICISM   AND   LOGIC 

question  whether  Homer  existed  ;  but  here  "  Homer  " 
means  "  the  author  of  the  Homeric  poems,"  and  is  a 
description.  Similarly  we  may  ask  whether  God  exists  ; 
but  then  "  God  "  means  "  the  Supreme  Being  "  or  "  the 
ens  realissimum  "  or  whatever  other  description  we  may 
prefer.  If  "  God  "  were  a  proper  name,  God  would  have 
to  be  a  datum  ;  and  then  no  question  could  arise  as  to 
His  existence.  The  distinction  between  existence  and 
other  predicates,  which  Kant  obscurely  felt,  is  brought 
to  light  by  the  theory  of  descriptions,  and  is  seen  to 
remove  "  existence  "  altogether  from  the  fundamental 
notions  of  metaphysics. 

What  has  been  said  about  "  existence  "  applies  equally 
to  "  reality,"  which  may,  in  fact,  be  taken  as  synonymous 
with  "  existence."  Concerning  the  immediate  objects  in 
illusions,  hallucinations,  and  dreams,  it  is  meaningless  to 
ask  whether  they  "  exist  "  or  are  "  real."  There  they  are, 
and  that  ends  the  matter.  But  we  may  legitimately 
inquire  as  to  the  existence  or  reality  of  "  things  "  or  other 
"  sensibilia  "  inferred  from  such  objects.  It  is  the  un- 
reality of  these  "  things  "  and  other  "  sensibilia,"  together 
with  a  failure  to  notice  that  they  are  not  data,  which  has 
led  to  the  view  that  the  objects  of  dreams  are  unreal. 

We  may  now  apply  these  considerations  in  detail  to  the 
stock  arguments  against  realism,  though  what  is  to  be  said 
will  be  mainly  a  repetition  of  what  others  have  said  before. 

(1)  We  have  first  the  variety  of  normal  appearances, 
supposed  to  be  incompatible.     This  is  the  case  of  the 
different  shapes  and  colours  which  a  given  thing  presents 
to  different  spectators.    Locke's  water  which  seems  both 
hot  and  cold  belongs  to  this  class  of  cases.    Our  system 
of  different  perspectives  fully  accounts  for  these  cases, 
and  shows  that  they  afford  no  argument  against  realism. 

(2)  We  have  cases   where    the    correlation    between 


SENSE-DATA   AND   PHYSICS  177 

different  senses  is  unusual.  The  bent  stick  in  water 
belongs  here.  People  say  it  looks  bent  but  is  straight : 
this  only  means  that  it  is  straight  to  the  touch,  though 
bent  to  sight.  There  is  no  "illusion,"  but  only  a  false 
inference,  if  we  think  that  the  stick  would  feel  bent  to 
the  touch.  The  stick  would  look  just  as  bent  in  a  photo- 
graph, and,  as  Mr.  Gladstone  used  to  say,  "  the  photo- 
graph cannot  lie."1  The  case  of  seeing  double  also 
belongs  here,  though  in  this  case  the  cause  of  the  unusual 
correlation  is  physiological,  and  would  therefore  not 
operate  in  a  photograph.  It  is  a  mistake  to  ask  whether 
the  "  thing  "  is  duplicated  when  we  see  it  double.  The 
"  thing  "  is  a  whole  system  of  "  sensibilia,"  and  it  is  only 
those  visual  "  sensibilia  "  which  are  data  to  the  per- 
cipient that  are  duplicated.  The  phenomenon  has  a 
purely  physiological  explanation  ;  indeed,  in  view  of  our 
having  two  eyes,  it  is  in  less  need  of  explanation  than  the 
single  visual  sense-datum  which  we  normally  obtain  from 
the  things  on  which  we  focus. 

(3)  We  come  now  to  cases  like  dreams,  which  may,  at 
the  moment  of  dreaming,  contain  nothing  to  arouse  sus- 
picion, but  are  condemned  on  the  ground  of  their  supposed 
incompatibility  with  earlier  and  later  data.  Of  course  it 
often  happens  that  dream-objects  fail  to  behave  in  the 
accustomed  manner  :  heavy  objects  fly,  solid  objects  melt, 
babies  turn  into  pigs  or  undergo  even  greater  changes. 
But  none  of  these  unusual  occurrences  need  happen  in  a 
dream,  and  it  is  not  on  account  of  such  occurrences  that 
dream-objects  are  called  "  unreal."  It  is  their  lack  of 
continuity  with  the  dreamer's  past  and  future  that  makes 
him,  when  he  wakes,  condemn  them  ;  and  it  is  their  lack 

1  Cf .  Edwin  B.  Holt,  The  Place  of  Illusory  Experience  in  a  Realistic 
World,  "  The  New  Realism,"  p.  305,  both  on  this  point  and  as  regards 
seeing  double. 


178  MYSTICISM   AND  LOGIC 

of  correlation  with  other  private  worlds  that  makes 
others  condemn  them.  Omitting  the  latter  ground,  our 
reason  for  condemning  them  is  that  the  "  things  "  which 
we  infer  from  them  cannot  be  combined  according  to  the 
laws  of  physics  with  the  "  things  "  inferred  from  waking 
sense-data.  This  might  be  used  to  condemn  the  "  things  " 
inferred  from  the  data  of  dreams.  Dream-data  are  no 
doubt  appearances  of  "  things,"  but  not  of  such  "  things  " 
as  the  dreamer  supposes.  I  have  no  wish  to  combat 
psychological  theories  of  dreams,  such  as  those  of  the 
psycho-analysts.  But  there  certainly  are  cases  where 
(whatever  psychological  causes  may  contribute)  the 
presence  of  physical  causes  also  is  very  evident.  For 
instance,  a  door  banging  may  produce  a  dream  of  a  naval 
engagement,  with  images  of  battleships  and  sea  and  smoke. 
The  whole  dream  will  be  an  appearance  of  the  door  bang- 
ing, but  owing  to  the  peculiar  condition  of  the  body 
(especially  the  brain)  during  sleep,  this  appearance  is  not 
that  expected  to  be  produced  by  a  door  banging,  and  thus 
the  dreamer  is  led  to  entertain  false  beliefs.  But  his 
sense-data  are  still  physical,  and  are  such  as  a  completed 
physics  would  include  and  calculate. 

(4)  The  last  class  of  illusions  are  those  which 
cannot  be  discovered  within  one  person's  experience, 
except  through  the  discovery  of  discrepancies  with 
the  experiences  of  others.  Dreams  might  conceivably 
belong  to  this  class,  if  they  were  jointed  sufficiently 
neatly  into  waking  life ;  but  the  chief  instances 
are  recurrent  sensory  hallucinations  of  the  kind 
that  lead  to  insanity.  What  makes  the  patient,  in  such 
cases,  become  what  others  call  insane  is  the  fact  that, 
within  his  own  experience,  there  is  nothing  to  show  that 
the  hallucinatory  sense-data  do  not  have  the  usual  kind 
of  connection  with  "  sensibilia  "  in  other  perspectives. 
Of  course  he  may  learn  this  through  testimony,  but  he 


SENSE-DATA   AND   PHYSICS  179 

probably  finds  it  simpler  to  suppose  that  the  testimony  is 
untrue  and  that  he  is  being  wilfully  deceived.  There  is, 
so  far  as  I  can  see,  no  theoretical  criterion  by  which  the 
patient  can  decide,  in  such  a  case,  between  the  two 
equally  satisfactory  hypotheses  of  his  madness  and  of  his 
friends'  mendacity. 

From  the  above  instances  it  would  appear  that  ab- 
normal sense-data,  of  the  kind  which  we  regard  as  decep- 
tive, have  intrinsically  just  the  same  status  as  any  others, 
but  differ  as  regards  their  correlations  or  causal  connec- 
tions with  other  "  sensibilia  "  and  with  "  things."  Since 
the  usual  correlations  and  connections  become  part  of 
our  unreflective  expectations,  and  even  seem,  except  to 
the  psychologist,  to  form  part  of  our  data,  it  comes  to  be 
thought,  mistakenly,  that  in  such  cases  the  data  are  un- 
real, whereas  they  are  merely  the  causes  of  false  infer- 
ences. The  fact  that  correlations  and  connections  of  un- 
usual kinds  occur  adds  to  the  difficulty  of  inferring  things 
from  sense  and  of  expressing  physics  in  terms  of  sense- 
data.  But  the  unusualness  would  seem  to  be  always 
physically  or  physiologically  explicable,  and  therefore 
raises  only  a  complication,  not  a  philosophical  objection. 

I  conclude,  therefore,  that  no  valid  objection  exists  to 
the  view  which  regards  sense-data  as  part  of  the  actual 
substance  of  the  physical  world,  and  that,  on  the  other 
hand,  this  view  is  the  only  one  which  accounts  for  the 
empirical  verifiability  of  physics.  In  the  present  paper, 
I  have  given  only  a  rough  preliminary  sketch.  In  par- 
ticular, the  part  played  by  time  in  the  construction  of  the 
physical  world  is,  I  think,  more  fundamental  than  would 
appear  from  the  above  account.  I  should  hope  that, 
with  further  elaboration,  the  part  played  by  unper- 
ceived  "  sensibilia  "  could  be  indefinitely  diminished, 
probably  by  invoking  the  history  of  a  "  thing  "  to  eke  out 
the  inferences  derivable  from  its  momentary  appearance. 


IX 

ON  THE   NOTION   OF  CAUSE 

IN  the  following  paper  I  wish,  first,  to  maintain  that 
the  word  "  cause  "  is  so  inextricably  bound  up  with 
misleading  associations  as  to  make  its  complete  extrusion 
from  the  philosophical  vocabulary  desirable  ;  secondly, 
to  inquire  what  principle,  if  any,  is  employed  in  science 
in  place  of  the  supposed  "  law  of  causality  "  which  philo- 
sophers imagine  to  be  employed ;  thirdly,  to  exhibit 
certain  confusions,  especially  in  regard  to  teleology  and 
determinism,  which  appear  to  me  to  be  connected  with 
erroneous  notions  as  to  causality. 

All  philosophers,  of  every  school,  imagine  that  causa- 
tion is  one  of  the  fundamental  axioms  or  postulates  of 
science,  yet,  oddly  enough,  in  advanced  sciences  such  as 
gravitational  astronomy,  the  word  "  cause  "  never  occurs. 
Dr.  James  Ward,  in  his  Naturalism  and  Agnosticism, 
makes  this  a  ground  of  complaint  against  physics :  the 
business  of  those  who  wish  to  ascertain  the  ultimate  truth 
about  the  world,  he  apparently  thinks,  should  be  the 
discovery  of  causes,  yet  physics  never  even  seeks  them. 
To  me  it  seems  that  philosophy  ought  not  to  assume  such 
legislative  functions,  and  that  the  reason  why  physics 
has  ceased  to  look  for  causes  is  that,  in  fact,  there  are  no 
such  things.  The  law  of  causality,  I  believe,  like  much 
that  passes  muster  among  philosophers,  is  a  relic  of  a 
bygone  age,  surviving,  like  the  monarchy,  only  because 
it  is  erroneously  supposed  to  do  no  harm. 


ON  THE   NOTION   OF  CAUSE  iSi 

In  order  to  find  out  what  philosophers  commonly 
understand  by  "  cause,"  I  consulted  Baldwin's  Dictionary, 
and  was  rewarded  beyond  my  expectations,  for  I  found 
the  following  three  mutually  incompatible  definitions  : — 

"  CAUSALITY,  (i)  The  necessary  connection  of  events 
in  the  time-series.  .  .  . 

"  CAUSE  (notion  of).  Whatever  may  be  included  in 
the  thought  or  perception  of  a  process  as  taking 
place  in  consequence  of  another  process.  .  .  . 

"  CAUSE  AND  EFFECT,  (i)  Cause  and  effect  .  .  .  are 
correlative  terms  denoting  any  two  distinguish- 
able things,  phases,  or  aspects  of  reality,  which 
are  so  related  to  each  other  that  whenever  the 
first  ceases  to  exist  the  second  comes  into  exist- 
ence immediately  after,  and  whenever  the  second 
comes  into  existence  the  first  has  ceased  to  exist 
immediately  before." 

Let  us  consider  these  three  definitions  in  turn.  The 
first,  obviously,  is  unintelligible  without  a  definition  of 
"  necessary."  Under  this  head,  Baldwin's  Dictionary 
gives  the  following  : — 

"  NECESSARY.  That  is  necessary  which  not  only  is 
true,  but  would  be  true  under  all  circumstances. 
Something  more  than  brute  compulsion  is,  there- 
fore, involved  in  the  conception ;  there  is  a 
general  law  under  which  the  thing  takes  place." 

The  notion  of  cause  is  so  intimately  connected  with 
that  of  necessity  that  it  will  be  no  digression  to  linger 
over  the  above  definition,  with  a  view  to  discovering,  if 
possible,  some  meaning  of  which  it  is  capable  ;  for,  as  it 
stands,  it  is  very  far  from  having  any  definite  signification. 

The  first  point  to  notice  is  that,  if  any  meaning  is  to  be 
given  to  the  phrase  "  would  be  true  under  all  circum- 
stances," the  subject  of  it  must  be  a  pro  positional  nine- 


i82  MYSTICISM   AND   LOGIC 

tion,  not  a  proposition.1  A  proposition  is  simply  true  or 
false,  and  that  ends  the  matter  :  there  can  be  no  ques- 
tion of  "  circumstances."  "  Charles  I's  head  was  cut  off  " 
is  just  as  true  in  summer  as  in  winter,  on  Sundays  as  on 
Mondays.  Thus  when  it  is  worth  saying  that  something 
"  would  be  true  under  all  circumstances,"  the  something 
in  question  must  be  a  prepositional  function,  i.e.  an 
expression  containing  a  variable,  and  becoming  a  pro- 
position when  a  value  is  assigned  to  the  variable  ;  the 
varying  "  circumstances "  alluded  to  are  then  the 
different  values  of  which  the  variable  is  capable.  Thus  if 
"  necessary  "  means  "  what  is  true  under  all  circum- 
stances," then  "  if  x  is  a  man,  x  is  mortal  "  is  necessary, 
because  it  is  true  for  any  possible  value  of  x.  Thus  we 
should  be  led  to  the  following  definition  : — 

"  NECESSARY  is  a  predicate  of  a  prepositional  function, 
meaning  that  it  is  true  for  all  possible  values  of 
its  argument  or  arguments." 

Unfortunately,  however,  the  definition  in  Baldwin's 
Dictionary  says  that  what  is  necessary  is  not  only  "  true 
under  all  circumstances  "  but  is  also  "  true."  Now  these 
two  are  incompatible.  Only  propositions  can  be  "  true," 
and  only  prepositional  functions  can  be  "  true  under  all 
circumstances."  Hence  the  definition  as  it  stands  is 
nonsense.  What  is  meant  seems  to  be  this  :  "A  pro- 
position is  necessary  when  it  is  a  value  of  a  prepositional 
function  which  is  true  under  all  ciecumstances,  i.e.  for  all 
values  of  its  argument  or  arguments."  But  if  we  adopt 
this  definition,  the  same  proposition  will  be  necessary  or 
contingent  according  as  we  choose  one  or  other  of  its 

1  A  prepositional  function  is  an  expression  containing  a  variable,  or 
undetermined  constituent,  and  becoming  a  proposition  as  soon  as  a 
definite  value  is  assigned  to  the  variable.  Examples  are  :  "  A  is  A," 
"  *  is  a  number."  The  variable  is  called  the  argument  of  the  function. 


ON   THE   NOTION   OF   CAUSE  183 

terms  as  the  argument  to  our  propositional  function.  For 
example,  "  if  Socrates  is  a  man,  Socrates  is  mortal,"  is 
necessary  if  Socrates  is  chosen  as  argument,  but  not  if 
man  or  mortal  is  chosen.  Again,  "  if  Socrates  is  a  man, 
Plato  is  mortal,"  will  be  necessary  if  either  Socrates  or 
man  is  chosen  as  argument,  but  not  if  Plato  or  mortal  is 
chosen.  However,  this  difficulty  can  be  overcome  by 
specifying  the  constituent  which  is  to  be  regarded  as 
argument,  and  we  thus  arrive  at  the  following  definition  : 

"  A  proposition  is  necessary  with  respect  to  a  given 
constituent  if  it  remains  true  when  that  constituent  is 
altered  in  any  way  compatible  with  the  proposition  re- 
maining significant." 

We  may  now  apply  this  definition  to  the  definition  of 
causality  quoted  above.  It  is  obvious  that  the  argument 
must  be  the  time  at  which  the  earlier  event  occurs.  Thus 
an  instance  of  causality  will  be  such  as  :  "If  the  event 
el  occurs  at  the  time  tlt  it  will  be  followed  by  the  event 
ez."  This  proposition  is  intended  to  be  necessary  with 
respect  to  tlt  i.e.  to  remain  true  however  tl  may  be 
varied.  Causality,  as  a  universal  law,  will  then  be  the 
following  :  "  Given  any  event  e1}  there  is  an  event  ez 
such  that,  whenever  e±  occurs,  ez  occurs  later."  But 
before  this  can  be  considered  precise,  we  must  specify 
how  much  later  ez  is  to  occur.  Thus  the  principle  be- 
comes : — 

"  Given  any  event  elt  there  is  an  event  e^  and  a  time- 
interval  T  such  that,  whenever  e^  occurs,  ez  follows  after 
an  interval  T  ." 

I  am  not  concerned  as  yet  to  consider  whether  this  law 
is  true  or  false.  For  the  present,  I  am  merely  concerned 
to  discover  what  the  law  of  causality  is  supposed  to  be. 
I  pass,  therefore,  to  the  other  definitions  quoted  above. 


184  MYSTICISM   AND   LOGIC 

The  second  definition  need  not  detain  us  long,  for  two 
reasons.  First,  because  it  is  psychological :  not  the 
"  thought  or  perception  "  of  a  process,  but  the  process 
itself,  must  be  what  concerns  us  in  considering  causality. 
Secondly,  because  it  is  circular  :  in  speaking  of  a  process 
as  "  taking  place  in  consequence  of  "  another  process,  it 
introduces  the  very  notion  of  cause  which  was  to  be 
denned. 

The  third  definition  is  by  far  the  most  precise  ;  indeed 
as  regards  clearness  it  leaves  nothing  to  be  desired.  But 
a  great  difficulty  is  caused  by  the  temporal  contiguity  of 
cause  and  effect  which  the  definition  asserts.  No  two 
instants  are  contiguous,  since  the  time-series  is  compact ; 
hence  either  the  cause  or  the  effect  or  both  must,  if  the 
definition  is  correct,  endure  for  a  finite  time  ;  indeed,  by 
the  wording  of  the  definition  it  is  plain  that  both  are 
assumed  to  endure  for  a  finite  time.  But  then  we  are 
faced  with  a  dilemma  :  if  the  cause  is  a  process  involving 
change  within  itself,  we  shall  require  (if  causality  is  uni- 
versal) causal  relations  between  its  earlier  and  later  parts  ; 
moreover,  it  would  seem  that  only  the  later  parts  can  be 
relevant  to  the  effect,  since  the  earlier  parts  are  not 
contiguous  to  the  effect,  and  therefore  (by  the  definition) 
cannot  influence  the  effect.  Thus  we  shall  be  led  to 
diminish  the  duration  of  the  cause  without  limit,  and 
however  much  we  may  diminish  it,  there  will  still 
remain  an  earlier  part  which  might  be  altered  without 
altering  the  effect,  so  that  the  true  cause,  as  defined,  will 
not  have  been  reached,  for  it  will  be  observed  that  the 
definition  excludes  plurality  of  causes.  If,  on  the  other 
hand,  the  cause  is  purely  static,  involving  no  change 
within  itself,  then,  in  the  first  place,  no  such  cause  is  to 
be  found  in  nature,  and  in  the  second  place,  it  seems 
strange — too  strange  to  be  accepted,  in  spite  of  bare 


ON   THE   NOTION   OF   CAUSE  185 

logical  possibility — that  the  cause,  after  existing  placidly 
for  some  time,  should  suddenly  explode  into  the  effect, 
when  it  might  just  as  well  have  done  so  at  any  earlier 
time,  or  have  gone  on  unchanged  without  producing  its 
effect.  This  dilemma,  therefore,  is  fatal  to  the  view  that 
cause  and  effect  can  be  contiguous  in  time  ;  if  there  are 
causes  and  effects,  they  must  be  separated  by  a  finite 
time-interval  r,  as  was  assumed  in  the  above  inter- 
pretation of  the  first  definition. 

What  is  essentially  the  same  statement  of  the  law  of 
causality  as  the  one  elicited  above  from  the  first  of 
Baldwin's  definitions  is  given  by  other  philosophers. 
Thus  John  Stuart  Mill  says  : — 

"  The  Law  of  Causation,  the  recognition  of  which  is  the 
main  pillar  of  inductive  science,  is  but  the  familiar  truth, 
that  invariability  of  succession  is  found  by  observation 
to  obtain  between  every  fact  in  nature  and  some  other 
fact  which  has  preceded  it."1 

And  Bergson,  who  has  rightly  perceived  that  the  law 
as  stated  by  philosophers  is  worthless,  nevertheless  con- 
tinues to  suppose  that  it  is  used  in  science.  Thus  he 
says : — 

"  Now,  it  is  argued,  this  law  [the  law  of  causality] 
means  that  every  phenomenon  is  determined  by  its 
conditions,  or,  in  other  words,  that  the  same  causes 
produce  the  same  effects."  2 

And  again  : — • 

"  We  perceive  physical  phenomena,  and  these  pheno- 
mena obey  laws.  This  means  :  (i)  That  phenomena 
a,  b,  c,  d,  previously  perceived,  can  occur  again  in  the 
same  shape  ;  (2)  that  a  certain  phenomenon  P,  which 

1  Logic,  Bk.  Ill,  Chap.  V,  §  2. 
:  Time  and  Free  Witt,  p.  199. 


186  MYSTICISM   AND   LOGIC 

appeared  after  the  conditions  a,  b,  c,  d,  and  after  these 
conditions  only,  will  not  fail  to  recur  as  soon  as  the  same 
conditions  are  again  present."1 

A  great  part  of  Bergson's  attack  on  science  rests  on  the 
assumption  that  it  employs  this  principle.  In  fact,  it 
employs  no  such  principle,  but  philosophers — even 
Bergson — are  too  apt  to  take  their  views  on  science  from 
each  other,  not  from  science.  As  to  what  the  principle 
is,  there  is  a  fair  consensus  among  philosophers  of  different 
schools.  There  are,  however,  a  number  of  difficulties 
which  at  once  arise.  I  omit  the  question  of  plurality  of 
causes  for  the  present,  since  other  graver  questions  have 
to  be  considered.  Two  of  these,  which  are  forced  on  our 
attention  by  the  above  statement  of  the  law,  are  the 
following : — 

(1)  What  is  meant  by  an  "  event  "  ? 

(2)  How  long  may  the  time-interval  be  between  cause 

and  effect  ? 

(i)  An  "event,"  in  the  statement  of  the  law,  is  ob- 
viously intended  to  be  something  that  is  likely  to  recur, 
since  otherwise  the  law  becomes  trivial.  It  follows  that 
an  "  event  "  is  not  a  particular,  but  some  universal  of 
which  there  may  be  many  instances.  It  follows  also  that 
an  "  event  "  must  be  something  short  of  the  whole  state 
of  the  universe,  since  it  is  highly  improbable  that  this  will 
recur.  What  is  meant  by  an  "  event  "  is  something  like 
striking  a  match,  or  dropping  a  penny  into  the  slot  of  an 
automatic  machine.  If  such  an  event  is  to  recur,  it  must 
not  be  defined  too  narrowly  :  we  must  not  state  with 
what  degree  of  force  the  match  is  to  be  struck,  nor  what 
is  to  be  the  temperature  of  the  penny.  For  if  such  con- 
siderations were  relevant,  our  "  event "  would  occur  at 

1  Time  and  Free  Will,  p.  202. 


ON   THE   NOTION   OF   CAUSE  187 

most  once,  and  the  law  would  cease  to  give  information. 
An  "  event,"  then,  is  a  universal  denned  sufficiently 
widely  to  admit  of  many  particular  occurrences  in  time 
being  instances  of  it. 

(2)  The  next  question  concerns  the  time-interval. 
Philosophers,  no  doubt,  think  of  cause  and  effect  as 
contiguous  in  time,  but  this,  for  reasons  already  given,  is 
impossible.  Hence,  since  there  are  no  infinitesimal  time- 
intervals,  there  must  be  some  finite  lapse  of  time  T 
between  cause  and  effect.  This,  however,  at  once  raises 
insuperable  difficulties.  However  short  we  make  the 
interval  r,  something  may  happen  during  this  interval 
which  prevents  the  expected  result.  I  put  my  penny  in 
the  slot,  but  before  I  can  draw  out  my  ticket  there  is  an 
earthquake  which  upsets  the  machine  and  my  calcula- 
tions. In  order  to  be  sure  of  the  expected  effect,  we 
must  know  that  there  is  nothing  in  the  environment  to 
interfere  with  it.  But  this  means  that  the  supposed 
cause  is  not,  by  itself,  adequate  to  insure  the  effect. 
And  as  soon  as  we  include  the  environment,  the  prob- 
ability of  repetition  is  diminished,  until  at  last,  when  the 
whole  environment  is  included,  the  probability  of  repeti- 
tion becomes  almost  nil. 

In  spite  of  these  difficulties,  it  must,  of  course,  be 
admitted  that  many  fairly  dependable  regularities  of 
sequence  occur  in  daily  life.  It  is  these  regularities  that 
have  suggested  the  supposed  law  of  causality  ;  where  they 
arc  found  to  fail,  it  is  thought  that  a  better  formulation 
could  have  been  found  which  would  have  never  failed. 
I  am  far  from  denying  that  there  may  be  such  sequences 
which  in  fact  never  do  fail.  It  may  be  that  there  will 
never  be  an  exception  to  the  rule  that  when  a  stone  of 
more  than  a  certain  mass,  moving  with  more  than  a 
certain  velocity,  comes  in  contact  with  a  pane  of  glass  of 


i88  MYSTICISM   AND   LOGIC 

less  than  a  certain  thickness,  the  glass  breaks.  I  also  do 
not  deny  that  the  observation  of  such  regularities,  even 
when  they  are  not  without  exceptions,  is  useful  in  the 
infancy  of  a  science  :  the  observation  that  unsupported 
bodies  in  air  usually  fall  was  a  stage  on  the  way  to  the 
law  of  gravitation.  What  I  deny  is  that  science  assumes 
the  existence  of  invariable  uniformities  of  sequence  of 
this  kind,  or  that  it  aims  at  discovering  them.  All  such 
uniformities,  as  we  saw,  depend  upon  a  certain  vagueness 
in  the  definition  of  the  "  events."  That  bodies  fall  is  a 
vague  qualitative  statement ;  science  wishes  to  know 
how  fast  they  fall.  This  depends  upon  the  shape  of  the 
bodies  and  the  density  of  the  air.  It  is  true  that  there  is 
more  nearly  uniformity  when  they  fall  in  a  vacuum  ;  so 
far  as  Galileo  could  observe,  the  uniformity  is  then  com- 
plete. But  later  it  appeared  that  even  there  the  latitude 
made  a  difference,  and  the  altitude.  Theoretically,  the 
position  of  the  sun  and  moon  must  make  a  difference. 
In  short,  every  advance  in  a  science  takes  us  farther 
away  from  the  crude  uniformities  which  are  first  observed, 
into  greater  differentiation  of  antecedent  and  consequent, 
and  into  a  continually  wider  circle  of  antecedents  recog- 
nised as  relevant. 

The  principle  "  same  cause,  same  effect,"  which  philo- 
sophers imagine  to  be  vital  to  science,  is  therefore  utterly 
otiose.  As  soon  as  the  antecedents  have  been  given 
sufficiently  fully  to  enable  the  consequent  to  be  calcu- 
lated with  some  exactitude,  the  antecedents  have  be- 
come so  complicated  that  it  is  very  unlikely  they  will 
ever  recur.  Hence,  if  this  were  the  principle  involved, 
science  would  remain  utterly  sterile. 

The  importance  of  these  considerations  lies  partly  in 
the  fact  that  they  lead  to  a  more  correct  account  of 
scientific  procedure,  partly  in  the  fact  that  they  remove 


ON   THE   NOTION   OF  CAUSE  189 

the  analogy  with  human  volition  which  makes  the  con- 
ception of  cause  such  a  fruitful  source  of  fallacies.  The 
latter  point  will  become  clearer  by  the  help  of  some 
illustrations.  For  this  purpose  I  shall  consider  a  few 
maxims  which  have  played  a  great  part  in  the  history  of 
philosophy. 

(1)  "  Cause  and  effect  must  more  or  less  resemble  each 
other."    This  principle  was  prominent  in  the  philosophy 
of  occasionalism,  and  is  still  by  no  means  extinct.    It  is 
still  often  thought,  for  example,  that  mind  could  not 
have  grown  up  in  a  universe  which  previously  contained 
nothing  mental,  and  one  ground  for  this  belief  is  that 
matter  is  too  dissimilar  from  mind  to  have  been  able  to 
cause  it.     Or,  more  particularly,  what  are  termed  the 
nobler  parts  of  our  nature  are  supposed  to  be  inexplicable, 
unless  the  universe  always  contained  something  at  least 
equally  noble  which  could  cause  them.    All  such  views 
seem  to  depend  upon  assuming  some  unduly  simplified 
law  of  causality  ;  for,  in  any  legitimate  sense  of  "  cause  " 
and   "effect,"   science   seems   to   show  that   they  are 
usually  very  widely  dissimilar,  the  "  cause  "  being,  in 
fact,  two  states  of  the  whole  universe,  and  the  "  effect  " 
some  particular  event. 

(2)  "  Cause  is  analogous  to  volition,  since  there  must 
be  an  intelligible  nexus  between  cause  and  effect."    This 
maxim  is,  I  think,  often  unconsciously  in  the  imagina- 
tions of  philosophers  who  would  reject  it  when  explicitly 
stated.     It  is  probably  operative  in  the  view  we  have 
just  been  considering,  that  mind  could  not  have  resulted 
from  a  purely  material  world.    I  do  not  profess  to  know 
what  is  meant  by  "  intelligible  "  ;    it  seems  to  mean 
"familiar  to  imagination."     Nothing  is  less  "intelli- 
gible," in  any  other  sense,  than  the  connection  between 


190  MYSTICISM    AND   LOGIC 

an  act  of  will  and  its  fulfilment.  But  obviously  the  sort 
of  nexus  desired  between  cause  and  effect  is  such  as  could 
only  hold  between  the  "events"  which  the  supposed 
law  of  causality  contemplates  ;  the  laws  which  replace 
causality  in  such  a  science  as  physics  leave  no  room  for 
any  two  events  between  which  a  nexus  could  be  sought. 

(3)  "  The  cause  compels  the  effect  in  some  sense  in 
which  the  effect  does  not  compel  the  cause."  This  belief 
seems  largely  operative  in  the  dislike  of  determinism  ; 
but,  as  a  matter  of  fact,  it  is  connected  with  our  second 
maxim,  and  falls  as  soon  as  that  is  abandoned.  We  may 
define  "  compulsion  "  as  follows  :  "  Any  set  of  circum- 
stances is  said  to  compel  A  when  A  desires  to  do  some- 
thing which  the  circumstances  prevent,  or  to  abstain 
from  something  which  the  circumstances  cause."  This 
presupposes  that  some  meaning  has  been  found  for  the 
word  "  cause  " — a  point  to  which  I  shall  return  later. 
What  I  want  to  make  clear  at  present  is  that  compulsion 
is  a  very  complex  notion,  involving  thwarted  desire.  So 
long  as  a  person  does  what  he  wishes  to  do,  there  is  no 
compulsion,  however  much  his  wishes  may  be  calculable 
by  the  help  of  earlier  events.  And  where  desire  does  not 
come  in,  there  can  be  no  question  of  compulsion.  Hence 
it  is,  in  general,  misleading  to  regard  the  cause  as  com- 
pelling the  effect. 

A  vaguer  form  of  the  same  fnaxim  substitutes  the  word 
"  determine  "  for  the  word  "  compel  "  ;  we  are  told  that 
the  cause  determines  the  effect  in  a  sense  in  which  the 
effect  does  not  determine  the  cause.  It  is  not  quite  clear 
what  is  meant  by  "  determining  "  ;  the  only  precise 
sense,  so  far  as  I  know,  is  that  of  a  function  or  one-many 
relation.  If  we  admit  plurality  of  causes,  but  not  of 
effects,  that  is,  if  we  suppose  that,  given  the  cause,  the 
effect  must  be  such  and  such,  but,  given  the  effect,  the 


ON  THE   NOTION   OF  CAUSE  191 

cause  may  have  been  one  of  many  alternatives,  then  we 
may  say  that  the  cause  determines  the  effect,  but  not  the 
effect  the  cause.  Plurality  of  causes,  however,  results 
only  from  conceiving  the  effect  vaguely  and  narrowly 
and  the  cause  precisely  and  widely.  Many  antecedents 
may  "  cause  "  a  man's  death,  because  his  death  is  vague 
and  narrow.  But  if  we  adopt  the  opposite  course,  taking 
as  the  "  cause  "  the  drinking  of  a  dose  of  arsenic,  and  as 
the  "  effect  "  the  whole  state  of  the  world  five  minutes 
later,  we  shall  have  plurality  of  effects  instead  of  plurality 
of  causes.  Thus  the  supposed  lack  of  symmetry  between 
"  cause  "  and  "  effect  "  is  illusory. 

(4)  "  A  cause  cannot  operate  when  it  has  ceased  to 
exist,  because  what  has  ceased  to  exist  is  nothing."  This 
is  a  common  maxim,  and  a  still  more  common  unex- 
pressed prejudice.  It  has,  I  fancy,  a  good  deal  to  do 
with  the  attractiveness  of  Bergson's  "  duree  "  :  since  the 
past  has  effects  now,  it  must  still  exist  in  some  sense. 
The  mistake  in  this  maxim  consists  in  the  supposition 
that  causes  "operate"  at  all.  A  volition  "operates" 
when  what  it  wills  takes  place  ;  but  nothing  can  operate 
except  a  volition.  The  belief  that  causes  "operate" 
results  from  assimilating  them,  consciously  or  uncon- 
sciously, to  volitions.  We  have  already  seen  that,  if 
there  are  causes  at  all,  they  must  be  separated  by  a  finite 
interval  of  time  from  their  effects,  and  thus  cause  their 
effects  after  they  have  ceased  to  exist. 

It  may  be  objected  to  the  above  definition  of  a  volition 
"  operating  "  that  it  only  operates  when  it  "  causes  " 
what  it  wills,  not  when  it  merely  happens  to  be  followed 
by  what  it  wills.  This  certainly  represents  the  usual  view 
of  what  is  meant  by  a  volition  "operating,"  but  as  it 
involves  the  very  view  of  causation  which  we  are  engaged 
in  combating,  it  is  not  open  to  us  as  a  definition.  We 


192  MYSTICISM   AND   LOGIC 

may  say  that  a  volition  "  operates  "  when  there  is  some 
law  in  virtue  of  which  a  similar  volition  in  rather  similar 
circumstances  will  usually  be  followed  by  what  it  wills. 
But  this  is  a  vague  conception,  and  introduces  ideas 
which  we  have  not  yet  considered.  What  is  chiefly  im- 
portant to  notice  is  that  the  usual  notion  of  "  operating  " 
is  not  open  to  us  if  we  reject,  as  I  contend  that  we  should, 
the  usual  notion  of  causation. 

(5)  "  A  cause  cannot  operate  except  where  it  is."  This 
maxim  is  very  widespread  ;  it  was  urged  against  Newton, 
and  has  remained  a  source  of  prejudice  against  "  action  at 
a  distance."  In  philosophy  it  has  led  to  a  denial  of 
transient  action,  and  thence  to  monism  or  Leibnizian 
monadism.  Like  the  analogous  maxim  concerning  tem- 
poral contiguity,  it  rests  upon  the  assumption  that  causes 
"  operate,"  i.e.  that  they  are  in  some  obscure  way 
analogous  to  volitions.  And,  as  in  the  case  of  temporal 
contiguity,  the  inferences  drawn  from  this  maxim  are 
wholly  groundless. 

I  return  now  to  the  question,  What  law  or  laws 
can  be  found  to  take  the  place  of  the  supposed  law  of 
causality  ? 

First,  without  passing  beyond  such  uniformities  of 
sequence  as  are  contemplated  by  the  traditional  law,  we 
may  admit  that,  if  any  such  sequence  has  been  observed 
in  a  great  many  cases,  and  has  never  been  found  to  fail, 
there  is  an  inductive  probability  that  it  will  be  found  to 
hold  in  future  cases.  If  stones  have  hitherto  been  found 
to  break  windows,  it  is  probable  that  they  will  continue 
to  do  so.  This,  of  course,  assumes  the  inductive  principle, 
of  which  the  truth  may  reasonably  be  questioned ;  but 
as  this  principle  is  not  our  present  concern,  I  shall  in  this 
discussion  treat  it  as  indubitable.  We  may  then  say,  in 
the  case  of  any  such  frequently  observed  sequence,  that 


ON   THE   NOTION   OF   CAUSE  193 

the  earlier  event  is  the  cause  and  the  later  event  the 
effect. 

Several  considerations,  however,  make  such  special 
sequences  very  different  from  the  traditional  relation  of 
cause  and  effect.  In  the  first  place,  the  sequence,  in  any 
hitherto  unobserved  instance,  is  no  more  than  probable, 
whereas  the  relation  of  cause  and  effect  was  supposed  to 
be  necessary.  I  do  not  mean  by  this  merely  that  we  are 
not  sure  of  having  discovered  a  true  case  of  cause  and 
effect ;  I  mean  that,  even  when  we  have  a  case  of  cause 
and  effect  in  our  present  sense,  all  that  is  meant  is  that 
on  grounds  of  observation,  it  is  probable  that  when  one 
occurs  the  other  will  also  occur.  Thus  in  our  present 
sense,  A  may  be  the  cause  of  B  even  if  there  actually  are 
cases  where  B  does  not  follow  A.  Striking  a  match  will 
be  the  cause  of  its  igniting,  in  spite  of  the  fact  that  some 
matches  are  damp  and  fail  to  ignite. 

In  the  second  place,  it  will  not  be  assumed  that  every 
event  has  some  antecedent  which  is  its  cause  in  this 
sense ;  we  shall  only  believe  in  causal  sequences  where 
we  find  them,  without  any  presumption  that  they  always 
are  to  be  found. 

In  the  third  place,  any  case  of  sufficiently  frequent 
sequence  will  be  causal  in  our  present  sense  ;  for  example, 
we  shall  not  refuse  to  say  that  night  is  the  cause  of  day. 
Our  repugnance  to  saying  this  arises  from  the  ease  with 
which  we  can  imagine  the  sequence  to  fail,  but  owing  to 
the  fact  that  cause  and  effect  must  be  separated  by  a 
finite  interval  of  time,  any  such  sequence  might  fail 
through  the  interposition  of  other  circumstances  in  the 
interval.  Mill,  discussing  this  instance  of  night  and  day, 
says  : — 

"  It  is  necessary  to  our  using  the  word  cause,  that  we 
should  believe  not  only  that  the  antecedent  always  has 
.  o 


194  MYSTICISM   AND   LOGIC 

been  followed  by  the  consequent,  but  that  as  long  as  the 
present  constitution  of  things  endures,  it  always  will 
be  so."1 

In  this  sense,  we  shall  have  to  give  up  the  hope  of  find- 
ing causal  laws  such  as  Mill  contemplated  ;  any  causal 
sequence  which  we  have  observed  may  at  any  moment  be 
falsified  without  a  falsification  of  any  laws  of  the  kind 
that  the  more  advanced  sciences  aim  at  establishing. 

In  the  fourth  place,  such  laws  of  probable  sequence, 
though  useful  in  daily  life  and  in  the  infancy  of  a  science, 
tend  to  be  displaced  by  quite  different  laws  as  soon  as  a 
science  is  successful.  The  law  of  gravitation  will  illustrate 
what  occurs  in  any  advanced  science.  In  the  motions  of 
mutually  gravitating  bodies,  there  is  nothing  that  can  be 
called  a  cause,  and  nothing  that  can  be  called  an  effect ; 
there  is  merely  a  formula.  Certain  differential  equations 
can  be  found,  which  hold  at  every  instant  for  every 
particle  of  the  system,  and  which,  given  the  configuration 
and  velocities  at  one  instant,  or  the  configurations  at  two 
instants,  render  the  configuration  at  any  other  earlier  or 
later  instant  theoretically  calculable.  That  is  to  say,  the 
configuration  at  any  instant  is  a  function  of  that  instant 
and  the  configurations  at  two  given  instants.  This  state- 
ment holds  throughout  physics,  and  not  only  in  the  special 
case  of  gravitation.  But  there  is  nothing  that  could  be 
properly  called  "  cause  "  and  notning  that  could  be 
properly  called  "  effect  "  in  such  a  system. 

No  doubt  the  reason  why  the  old  "  law  of  causality  " 
has  so  long  continued  to  pervade  the  books  of  philo- 
sophers is  simply  that  the  idea  of  a  function  is  unfamiliar 
to  most  of  them,  and  therefore  they  seek  an  unduly 
simplified  statement.  There  is  no  question  of  repetitions 
of  the  "  same  "  cause  producing  the  "  same  "  effect ;  it 
1  Loc.  dt.,  §  6. 


ON  THE   NOTION   OF   CAUSE  195 

is  not  in  any  sameness  of  causes  and  effects  that  the  con- 
stancy of  scientific  law  consists,  but  in  sameness  of 
relations.  And  even  "  sameness  of  relations "  is  too 
simple  a  phrase  ;  "  sameness  of  differential  equations  " 
is  the  only  correct  phrase.  It  is  impossible  to  state  this 
accurately  in  non-mathematical  language ;  the  nearest 
approach  would  be  as  follows  :  "  There  is  a  constant 
relation  between  the  state  of  the  universe  at  any  instant 
and  the  rate  of  change  in  the  rate  at  which  any  part  of 
the  universe  is  changing  at  that  instant,  and  this  relation 
is  many-one,  i.e.  such  that  the  rate  of  change  in  the 
rate  of  change  is  determinate  when  the  state  of  the 
universe  is  given."  If  the  "  law  of  causality  "  is  to  be 
something  actually  discoverable  in  the  practice  of  science, 
the  above  proposition  has  a  better  right  to  the  name 
than  any  "  law  of  causality  "  to  be  found  in  the  books  of 
philosophers. 

In  regard  to  the  above  principle,  several  observations 
must  be  made — 

(1)  No  one  can  pretend  that  the  above  principle  is  a 
priori  or  self-evident  or  a  "  necessity  of  thought."    Nor 
is  it,  in  any  sense,  a  premiss  of  science  :  it  is  an  empirical 
generalisation  from  a  number  of  laws  which  are  them- 
selves empirical  generalisations. 

(2)  The  law  makes  no  difference  between  past  and 
future  :    the  future  "  determines  "  the  past  in  exactly 
the  same  sense  in  which  the  past  "  determines  "  the  future. 
The  word  "  determine,"  here,  has  a  purely  logical  signifi- 
cance :     a   certain   number   of   variables    "  determine " 
another  variable  if  that  other  variable  is  a  function  of 
them. 

(3)  The  law  will  not  be  empirically  verifiable  unless 
the  course  of  events  within  some  sufficiently  small  volume 


196  MYSTICISM   AND   LOGIC 

will  be  approximately  the  same  in  any  two  states  of  the 
universe  which  only  differ  in  regard  to  what  is  at  a  con- 
siderable distance  from  the  small  volume  in  question. 
For  example,  motions  of  planets  in  the  solar  system  must 
be  approximately  the  same  however  the  fixed  stars  may 
be  distributed,  provided  that  all  the  fixed  stars  are  very 
much  farther  from  the  sun  than  the  planets  are.  If 
gravitation  varied  directly  as  the  distance,  so  that  the 
most  remote  stars  made  the  most  difference  to  the 
motions  of  the  planets,  the  world  might  be  just  as  regular 
and  just  as  much  subject  to  mathematical  laws  as  it  is  at 
present,  but  we  could  never  discover  the  fact. 

(4)  Although  the  old  "  law  of  causality  "  is  not  assumed 
by  science,  something  which  we  may  call  the  "  uniformity 
of  nature  "  is  assumed,  or  rather  is  accepted  on  inductive 
grounds.  The  uniformity  of  nature  does  not  assert  the 
trivial  principle  "  same  cause,  same  effect,"  but  the 
principle  of  the  permanence  of  laws.  That  is  to  say, 
when  a  law  exhibiting,  e.g.  an  acceleration  as  a  function 
of  the  configuration  has  been  found  to  hold  throughout 
the  observable  past,  it  is  expected  that  it  will  continue 
to  hold  in  the  future,  or  that,  if  it  does  not  itself  hold, 
there  is  some  other  law,  agreeing  with  the  supposed  law 
as  regards  the  past,  which  will  hold  for  the  future.  The 
ground  of  this  principle  is  simply  the  inductive  ground 
that  it  has  been  found  to  be  true  in  very  many  instances  ; 
hence  the  principle  cannot  be  considered  certain,  but 
only  probable  to  a  degree  which  cannot  be  accurately 
estimated. 

The  uniformity  of  nature,  in  the  above  sense,  although 
it  is  assumed  in  the  practice  of  science,  must  not,  in  its 
generality,  be  regarded  as  a  kind  of  major  premiss,  with- 
out which  all  scientific  reasoning  would  be  in  error.  The 
assumption  that  all  laws  of  nature  are  permanent  has,  of 


ON  THE   NOTION   OF   CAUSE  197 

course,  less  probability  than  the  assumption  that  this  or 
that  particular  law  is  permanent ;  and  the  assumption 
that  a  particular  law  is  permanent  for  all  time  has  less 
probability  than  the  assumption  that  it  will  be  valid  up 
to  such  and  such  a  date.  Science,  in  any  given  case,  will 
assume  what  the  case  requires,  but  no  more.  In  con- 
structing the  Nautical  Almanac  for  1915  it  will  assume 
that  the  law  of  gravitation  will  remain  true  up  to  the  end 
of  that  year  ;  but  it  will  make  no  assumption  as  to  1916 
until  it  comes  to  the  next  volume  of  the  almanac.  This 
procedure  is,  of  course,  dictated  by  the  fact  that  the 
uniformity  of  nature  is  not  known  a  priori,  but  is  an 
empirical  generalisation,  like  "all  men  are  mortal."  In 
all  such  cases,  it  is  better  to  argue  immediately  from  the 
given  particular  instances  to  the  new  instance,  than  to 
argue  by  way  of  a  major  premiss  ;  the  conclusion  is  only 
probable  in  either  case,  but  acquires  a  higher  probability 
by  the  former  method  than  by  the  latter. 

In  all  science  we  have  to  distinguish  two  sorts  of  laws  : 
first,  those  that  are  empirically  verifiable  but  probably 
only  approximate  ;  secondly,  those  that  are  not  verifiable, 
but  may  be  exact.  The  law  of  gravitation,  for  example, 
in  its  applications  to  the  solar  system,  is  only  empirically 
verifiable  when  it  is  assumed  that  matter  outside  the 
solar  system  may  be  ignored  for  such  purposes  ;  we 
believe  this  to  be  only  approximately  true,  but  we  cannot 
empirically  verify  the  law  of  universal  gravitation  which 
we  believe  to  be  exact.  This  point  is  very  important  in 
connection  with  what  we  may  call  "  relatively  isolated 
systems."  These  may  be  defined  as  follows  : — 

A  system  relatively  isolated  during  a  given  period  is 
one  which,  within  some  assignable  margin  of  error,  will 
behave  in  the  same  way  throughout  that  period,  however 
the  rest  of  the  universe  may  be  constituted. 


198  MYSTICISM  AND   LOGIC 

A  system  may  be  called  "  practically  isolated  "  during  a 
given  period  if,  although  there  might  be  states  of  the  rest 
of  the  universe  which  would  produce  more  than  the 
assigned  margin  of  error,  there  is  reason  to  believe  that 
such  states  do  not  in  fact  occur. 

Strictly  speaking,  we  ought  to  specify  the  respect  in 
which  the  system  is  relatively  isolated.  For  example, 
the  earth  is  relatively  isolated  as  regards  falling  bodies, 
but  not  as  regards  tides  ;  it  is  practically  isolated  as 
regards  economic  phenomena,  although,  if  Jevons'  sun- 
spot  theory  of  commercial  crises  had  been  true,  it  would 
not  have  been  even  practically  isolated  in  this  respect. 

It  will  be  observed  that  we  cannot  prove  in  advance 
that  a  system  is  isolated.  This  will  be  inferred  from  the 
observed  fact  that  approximate  uniformities  can  be 
stated  for  this  system  alone.  If  the  complete  laws  for 
the  whole  universe  were  known,  the  isolation  of  a  system 
could  be  deduced  from  them  ;  assuming,  for  example, 
the  law  of  universal  gravitation,  the  practical  isolation  of 
the  solar  system  in  this  respect  can  be  deduced  by  the 
help  of  the  fact  that  there  is  very  little  matter  in  its 
neighbourhood.  But  it  should  be  observed  that  isolated 
systems  are  only  important  as  providing  a  possibility  of 
discovering  scientific  laws  ;  they  have  no  theoretical 
importance  in  the  finished  structure  of  a  science. 

The  case  where  one  event  A  is  said  to  "  cause  "  another 
event  B,  which  philosophers  take  as  fundamental,  is 
really  only  the  most  simplified  instance  of  a  practically 
isolated  system.  It  may  happen  that,  as  a  result  of 
general  scientific  laws,  whenever  A  occurs  throughout  a 
certain  period,  it  is  followed  by  B  ;  in  that  case,  A  and  B 
form  a  system  which  is  practically  isolated  throughout 
that  period.  It  is,  however,  to  be  regarded  as  a  piece  of 
good  fortune  if  this  occurs  ;  it  will  always  be  due  to  special 


ON   THE   NOTION   OF   CAUSE  199 

circumstances,  and  would  not  have  been  true  if  the  rest 
of  the  universe  had  been  different  though  subject  to  the 
same  laws. 

The  essential  function  which  causality  has  been  sup- 
posed to  perform  is  the  possibility  of  inferring  the  future 
from  the  past,  or,  more  generally,  events  at  any  time  from 
events  at  certain  assigned  times.  Any  system  in  which 
such  inference  is  possible  may  be  called  a  "  determin- 
istic "  system.  We  may  define  a  deterministic  system  as 
follows  : — 

A  system  is  said  to  be  "  deterministic  "  when,  given 
certain  data,  elt  e2,  . . .,  CH,  at  times  tlt  tz,  . . .,  tH  respec- 
tively, concerning  this  system,  if  E,  is  the  state  of  the 
system  at  any  time  t,  there  is  a  functional  relation  of  the 

form  E^fie^^e,,^,  ...,en,tn,t}.  (A) 

The  system  will  be  "  deterministic  throughout  a  given 
period  "  if  t,  in  the  above  formula,  may  be  any  time 
within  that  period,  though  outside  that  period  the 
formula  may  be  no  longer  true.  If  the  universe,  as  a 
whole,  is  such  a  system,  determinism  is  true  of  the 
universe  ;  if  not,  not.  A  system  which  is  part  of  a  deter- 
ministic system  I  shall  call  "  determined  "  ;  one  which  is 
not  part  of  any  such  system  I  shall  call  "  capricious." 

The  events  ev  ez,  . . .,  en  I  shall  call  "  determinants  " 
of  the  system.  It  is  to  be  observed  that  a  system  which 
has  one  set  of  determinants  will  in  general  have  many. 
In  the  case  of  the  motions  of  the  planets,  for  example, 
the  configurations  of  the  solar  system  at  any  two  given 
times  will  be  determinants. 

We  may  take  another  illustration  from  the  hypothesis 
of  psycho-physical  parallelism.  Let  us  assume,  for  the 
purposes  of  this  illustration,  that  to  a  given  state  of  brain 


200  MYSTICISM   AND   LOGIC 

a  given  state  of  mind  always  corresponds,  and  vice  versa, 
i.e.  that  there  is  a  one-one  relation  between  them,  so  that 
each  is  a  function  of  the  other.  We  may  also  assume, 
what  is  practically  certain,  that  to  a  given  state  of  a 
certain  brain  a  given  state  of  the  whole  material  universe 
corresponds,  since  it  is  highly  improbable  that  a  given 
brain  is  ever  twice  in  exactly  the  same  state.  Hence 
there  will  be  a  one-one  relation  between  the  state  of  a 
given  person's  mind  and  the  state  of  the  whole  material 
universe.  It  follows  that,  if  n  states  of  the  material 
universe  are  determinants  of  the  material  universe,  then 
n  states  of  a  given  man's  mind  are  determinants  of  the 
whole  material  and  mental  universe — assuming,  that  is 
to  say,  that  psycho-physical  parallelism  is  true. 

The  above  illustration  is  important  in  connection  with 
a  certain  confusion  which  seems  to  have  beset  those  who 
have  philosophised  on  the  relation  of  mind  and  matter 
It  is  often  thought  that,  if  the  state  of  the  mind  is  deter- 
minate when  the  state  of  the  brain  is  given,  and  if  the 
material  world  forms  a  deterministic  system,  then  mind 
is  "  subject  "  to  matter  in  some  sense  in  which  matter  is 
not  "  subject  "  to  mind.  But  if  the  state  of  the  brain  is 
also  determinate  when  the  state  of  the  mind  is  given,  it 
must  be  exactly  as  true  to  regard  matter  as  subject  to 
mind  as  it  would  be  to  regard  mind  as  subject  to  matter. 
We  could,  theoretically,  work  out  the  history  of  mind 
without  ever  mentioning  matter,  and  then,  at  the  end, 
deduce  that  matter  must  meanwhile  have  gone  through 
the  corresponding  history.  It  is  true  that  if  the  relation 
of  brain  to  mind  were  many-one,  not  one-one,  there  would 
be  a  one-sided  dependence  of  mind  on  brain,  while  con- 
versely, if  the  relation  were  one-many,  as  Bergson  sup- 
poses, there  would  be  a  one-sided  dependence  of  brain  on 
mind.  But  the  dependence  involved  is,  in  any  case,  only 


ON  THE   NOTION  OF  CAUSE  201 

logical ;  it  does  not  mean  that  we  shall  be  compelled  to 
do  things  we  desire  not  to  do,  which  is  what  people  in- 
stinctively imagine  it  to  mean. 

As  another  illustration  we  may  take  the  case  of 
mechanism  and  teleology.  A  system  may  be  defined  as 
"  mechanical  "  when  it  has  a  set  of  determinants  that 
are  purely  material,  such  as  the  positions  of  certain  pieces 
of  matter  at  certain  times.  It  is  an  open  question  whether 
the  world  of  mind  and  matter,  as  we  know  it,  is  a 
mechanical  system  or  not ;  let  us  suppose,  for  the  sake 
of  argument,  that  it  is  a  mechanical  system.  This  sup- 
position— so  I  contend — throws  no  light  whatever  on  the 
question  whether  the  universe  is  or  is  not  a  "  teleo- 
logical  "  system.  It  is  difficult  to  define  accurately  what 
is  meant  by  a  "  teleological  "  system,  but  the  argument 
is  not  much  affected  by  the  particular  definition  we  adopt. 
Broadly,  a  teleological  system  is  one  in  which  purposes 
are  realised,  i.e.  in  which  certain  desires — those  that  are 
deeper  or  nobler  or  more  fundamental  or  more  universal 
or  what  not — are  followed  by  their  realisation.  Now  the 
fact — if  it  be  a  fact — that  the  universe  is  mechanical  has 
no  bearing  whatever  on  the  question  whether  it  is  teleo- 
logical in  the  above  sense.  There  might  be  a  mechanical 
system  in  which  all  wishes  were  realised,  and  there  might 
be  one  in  which  all  wishes  were  thwarted.  The  question 
whether,  or  how  far,  our  actual  world  is  teleological, 
cannot,  therefore,  be  settled  by  proving  that  it  is  mechani- 
cal, and  the  desire  that  it  should  be  teleological  is  no 
ground  for  wishing  it  to  be  not  mechanical. 

There  is,  in  all  these  questions,  a  very  great  difficulty 
in  avoiding  confusion  between  what  we  can  infer  and 
what  is  in  fact  determined.  Let  us  consider,  for  a 
moment,  the  various  senses  in  which  the  future  may  be 
"  determined."  There  is  one  sense — and  a  very  important 


202  MYSTICISM   AND   LOGIC 

one — in  which  it  is  determined  quite  independently  of 
scientific  laws,  namely,  the  sense  that  it  will  be  what  it 
will  be.  We  all  regard  the  past  as  determined  simply  by 
the  fact  that  it  has  happened  ;  but  for  the  accident  that 
memory  works  backward  and  not  forward,  we  should 
regard  the  future  as  equally  determined  by  the  fact  that 
it  will  happen.  "  But,"  we  are  told,  "  you  cannot  alter 
the  past,  while  you  can  to  some  extent  alter  the  future." 
This  view  seems  to  me  to  rest  upon  just  those  errors  in 
regard  to  causation  which  it  has  been  my  object  to  remove. 
You  cannot  make  the  past  other  than  it  was — true,  but 
this  is  a  mere  application  of  the  law  of  contradiction.  If 
you  already  know  what  the  past  was,  obviously  it  is  use- 
less to  wish  it  different.  But  also  you  cannot  make  the 
future  other  than  it  will  be  ;  this  again  is  an  application 
of  the  law  of  contradiction.  And  if  you  happen  to  know 
the  future — e.g.  in  the  case  of  a  forthcoming  eclipse — it 
is  just  as  useless  to  wish  it  different  as  to  wish  the  past 
different.  "  But,"  it  will  be  rejoined,  "  our  wishes  can 
cause  the  future,  sometimes,  to  be  different  from  what  it 
would  be  if  they  did  not  exist,  and  they  can  have  no 
such  effect  upon  the  past."  This,  again,  is  a  mere 
tautology.  An  effect  being  defined  as  something  subse- 
quent to  its  cause,  obviously  we  can  have  no  effect  upon 
the  past.  But  that  does  not  mean  that  the  past  would 
not  have  been  different  if  our  present  wishes  had  been 
different.  Obviously,  our  present  wishes  are  conditioned 
by  the  past,  and  therefore  could  not  have  been  different 
unless  the  past  had  been  different ;  therefore,  if  our 
present  wishes  were  different,  the  past  would  be  different. 
Of  course,  the  past  cannot  be  different  from  what  it  was, 
but  no  more  can  our  present  wishes  be  different  from  what 
they  are  ;  this  again  is  merely  the  law  of  contradiction. 
The  facts  seem  to  be  merely  (i)  that  wishing  generally 


ON   THE  NOTION   OF   CAUSE  203 

depends  upon  ignorance,  and  is  therefore  commoner  in 
regard  to  the  future  than  in  regard  to  the  past  ;  (2)  that 
where  a  wish  concerns  the  future,  it  and  its  realisation 
very  often  form  a  "  practically  independent  system," 
i.e.  many  wishes  regarding  the  future  are  realised.  But 
there  seems  no  doubt  that  the  main  difference  in  our 
feelings  arises  from  the  accidental  fact  that  the  past 
but  not  the  future  can  be  known  by  memory. 

Although  the  sense  of  "  determined  "  in  which  the 
future  is  determined  by  the  mere  fact  that  it  will  be  what 
it  will  be  is  sufficient  (at  least  so  it  seems  to  me)  to  refute 
some  opponents  of  determinism,  notably  M.  Bergson  and 
the  pragmatists,  yet  it  is  not  what  most  people  have  in 
mind  when  they  speak  of  the  future  as  determined.  What 
they  have  in  mind  is  a  formula  by  means  of  which  the 
future  can  be  exhibited,  and  at  least  theoretically  calcu- 
lated, as  a  function  of  the  past.  But  at  this  point  we 
meet  with  a  great  difficulty,  which  besets  what  has  been 
said  above  about  deterministic  systems,  as  well  as  what 
is  said  by  others. 

If  formulae  of  any  degree  of  complexity,  however  great, 
are  admitted,  it  would  seem  that  any  system,  whose 
state  at  a  given  moment  is  a  function  of  certain  measur- 
able quantities,  must  be  a  deterministic  system.  Let  us 
consider,  in  illustration,  a  single  material  particle,  whose 
co-ordinates  at  time  t  are  x(,  yt,  zt.  Then,  however,  the 
particle  moves,  there  must  be,  theoretically,  functions 
/i.  fz>  /a.  such  that 


It  follows  that,  theoretically,  the  whole  state  of  the 
material  universe  at  time  t  must  be  capable  of  being 
exhibited  as  a  function  of  t.  Hence  our  universe  will  be 
deterministic  in  the  sense  denned  above.  But  if  this  be 


204  MYSTICISM   AND   LOGIC 

true,  no  information  is  conveyed  about  the  universe  in 
stating  that  it  is  deterministic.  It  is  true  that  the  formulae 
involved  may  be  of  strictly  infinite  complexity,  and  there- 
fore not  practically  capable  of  being  written  down  or 
apprehended.  But  except  from  the  point  of  view  of  our 
knowledge,  this  might  seem  to  be  a  detail :  in  itself,  if 
the  above  considerations  are  sound,  the  material  universe 
must  be  deterministic,  must  be  subject  to  laws. 

This,  however,  is  plainly  not  what  was  intended.  The 
difference  between  this  view  and  the  view  intended  may 
be  seen  as  follows.  Given  some  formula  which  fits  the 
facts  hitherto — say  the  law  of  gravitation — there  will  be 
an  infinite  number  of  other  formulae,  not  empirically  dis- 
tinguishable from  it  in  the  past,  but  diverging  from  it 
more  and  more  in  the  future.  Hence,  even  assuming 
that  there  are  persistent  laws,  we  shall  have  no  reason 
for  assuming  that  the  law  of  the  inverse  square  will  hold 
in  future  ;  it  may  be  some  other  hitherto  indistinguishable 
law  that  will  hold.  We  cannot  say  that  every  law  which 
has  held  hitherto  must  hold  in  the  future,  because  past 
facts  which  obey  one  law  will  also  obey  others,  hitherto 
indistinguishable  but  diverging  in  future.  Hence  there 
must,  at  every  moment,  be  laws  hitherto  unbroken  which 
are  now  broken  for  the  first  time.  What  science  does,  in 
fact,  is  to  select  the  simplest  formula  that  will  fit  the  facts. 
But  this,  quite  obviously,  is  merely  a  methodological 
precept,  not  a  law  of  Nature.  If  the  simplest  formula 
ceases,  after  a  time,  to  be  applicable,  the  simplest  formula 
that  remains  applicable  is  selected,  and  science  has  no 
sense  that  an  axiom  has  been  falsified.  We  are  thus  left 
with  the  brute  fact  that,  in  many  departments  of  science, 
quite  simple  laws  have  hitherto  been  found  to  hold.  This 
fact  cannot  be  regarded  as  having  any  a  priori  ground, 
nor  can  it  be  used  to  support  inductively  the  opinion  that 


ON   THE  NOTION   OF  CAUSE  205 

the  same  laws  will  continue  ;  for  at  every  moment  laws 
hitherto  true  are  being  falsified,  though  in  the  advanced 
sciences  these  laws  are  less  simple  than  those  that  have 
remained  true.  Moreover  it  would  be  fallacious  to  argue 
inductively  from  the  state  of  the  advanced  sciences  to  the 
future  state  of  the  others,  for  it  may  well  be  that  the 
advanced  sciences  are  advanced  simply  because,  hitherto, 
their  subject-matter  has  obeyed  simple  and  easily 
ascertainable  laws,  while  the  subject-matter  of  other 
sciences  has  not  done  so. 

The  difficulty  we  have  been  considering  seems  to  be 
met  partly,  if  not  wholly,  by  the  principle  that  the  time 
must  not  enter  explicitly  into  our  formulae.  All  mechanical 
laws  exhibit  acceleration  as  a  function  of  configuration, 
not  of  configuration  and  time  jointly  ;  and  this  principle 
of  the  irrelevance  of  the  time  may  be  extended  to  all 
scientific  laws.  In  fact  we  might  interpret  the  "  uni- 
formity of  nature  "  as  meaning  just  this,  that  no  scientific 
law  involves  the  time  as  an  argument,  unless,  of  course, 
it  is  given  in  an  integrated  form,  in  which  case  lapse  of 
time,  though  not  absolute  time,  may  appear  in  our 
formulae.  Whether  this  consideration  suffices  to  over- 
come our  difficulty  completely,  I  do  not  know ;  but  in 
any  case  it  does  much  to  diminish  it. 

It  will  serve  to  illustrate  what  has  been  said  if  we  apply 
it  to  the  question  of  free  will. 

(i)  Determinism  in  regard  to  the  will  is  the  doctrine 
that  our  volitions  belong  to  some  deterministic  system, 
i.e.  are  "  determined "  in  the  sense  defined  above. 
Whether  this  doctrine  is  true  or  false,  is  a  mere  question 
of  fact ;  no  a  priori  considerations  (if  our  previous  dis- 
cussions have  been  correct)  can  exist  on  either  side.  On 
the  one  hand,  there  is  no  a  priori  category  of  causality, 
but  merely  certain  observed  uniformities.  As  a  matter 


206  MYSTICISM   AND   LOGIC 

of  fact,  there  are  observed  uniformities  in  regard  to 
volitions ;  thus  there  is  some  empirical  evidence  that 
volitions  are  determined.  But  it  would  be  very  rash  to 
maintain  that  the  evidence  is  overwhelming,  and  it  is 
quite  possible  that  some  volitions,  as  well  as  some  other 
things,  are  not  determined,  except  in  the  sense  in  which 
we  found  that  everything  must  be  determined. 

(2)  But,  on  the  other  hand,  the  subjective  sense  of 
freedom,  sometimes  alleged  against  determinism,  has  no 
bearing  on  the  question  whatever.    The  view  that  it  has 
a  bearing  rests  upon  the  belief  that  causes  compel  their 
effects,  or  that  nature  enforces  obedience  to  its  laws  as 
governments    do.      These    are    mere    anthropomorphic 
superstitions,  due  to  assimilation  of  causes  with  volitions 
and  of  natural  laws  with  human  edicts.    We  feel  that  our 
will  is  not  compelled,  but  that  only  means  that  it  is  not 
other  than  we  choose  it  to  be.    It  is  one  of  the  demerits 
of  the  traditional  theory  of  causality  that  it  has  created 
an  artificial  opposition  between  determinism  and  the 
freedom  of  which  we  are  introspectively  conscious. 

(3)  Besides  the  general  question  whether  volitions  are 
determined,  there  is  the  further  question  whether  they 
are  mechanically  determined,  i.e.  whether  they  are  part 
of  what  was  above  defined  as  a  mechanical  system.    This 
is  the  question  whether  they  form  part  of  a  system  with 
purely  material  determinants,  i.e.  whether  there  are  laws 
which,  given  certain  material  data,  make  all  volitions 
functions  of  those  data.    Here  again,  there  is  empirical 
evidence  up  to  a  point,  but  it  is  not  conclusive  in  regard 
to  all  volitions.     It  is  important  to  observe,  however 
that  even  if  volitions  are  part  of  a  mechanical  system, 
this  by  no  means  implies  any  supremacy  of  matter  over 
mind.    It  may  well  be  that  the  same  system  which  is 


ON  THE   NOTION  OF  CAUSE  207 

susceptible  of  material  determinants  is  also  susceptible 
of  mental  determinants  ;  thus  a  mechanical  system  may 
be  determined  by  sets  of  volitions,  as  well  as  by  sets  of 
material  facts.  It  would  seem,  therefore,  that  the  reasons 
which  make  people  dislike  the  view  that  volitions  are 
mechanically  determined  are  fallacious. 

(4)  The  notion  of  necessity,  which  is  often  associated 
with  determinism,  is  a  confused  notion  not  legitimately 
deducible  from  determinism.  Three  meanings  are 
commonly  confounded  when  necessity  is  spoken  of  : — 

(a)  An  action  is  necessary  when  it  will  be  performed 
however  much  the  agent  may  wish  to  do  otherwise. 
Determinism  does  not  imply  that  actions  are  necessary 
in  this  sense. 

(/3)  A  propositional  function  is  necessary  when  all  its 
values  are  true.  This  sense  is  not  relevant  to  our  present 
discussion. 

(y)  A  proposition  is  necessary  with  respect  to  a  given 
constituent  when  it  is  the  value,  with  that  constituent  as 
argument,  of  a  necessary  propositional  function,  in  other 
words,  when  it  remains  true  however  that  constituent 
may  be  varied.  In  this  sense,  in  a  deterministic  system, 
the  connection  of  a  volition  with  its  determinants  is 
necessary,  if  the  time  at  which  the  determinants  occur  be 
taken  as  the  constituent  to  be  varied,  the  time-interval 
between  the  determinants  and  the  volition  being  kept 
constant.  But  this  sense  of  necessity  is  purely  logical, 
and  has  no  emotional  importance. 

We  may  now  sum  up  our  discussion  of  causality.  We 
found  first  that  the  law  of  causality,  as  usually  stated  by 
philosophers,  is  false,  and  is  not  employed  in  science.  We 
then  considered  the  nature  of  scientific  laws,  and  found 
that,  instead  of  stating  that  one  event  A  is  always  followed 


208  MYSTICISM   AND   LOGIC 

by  another  event  B,  they  stated  functional  relations 
between  certain  events  at  certain  times,  which  we  called 
determinants,  and  other  events  at  earlier  or  later  times 
or  at  the  same  time.  We  were  unable  to  find  any  a  priori 
category  involved  :  the  existence  of  scientific  laws  ap- 
peared as  a  purely  empirical  fact,  not  necessarily  universal, 
except  in  a  trivial  and  scientifically  useless  form.  We 
found  that  a  system  with  one  set  of  determinants  may  very 
likely  have  other  sets  of  a  quite  different  kind,  that,  for 
example,  a  mechanically  determined  system  may  also  be 
ideologically  or  volitionally  determined.  Finally  we 
considered  the  problem  of  free  will :  here  we  found  that 
the  reasons  for  supposing  volitions  to  be  determined  are 
strong  but  not  conclusive,  and  we  decided  that  even  if 
volitions  are  mechanically  determined,  that  is  no  reason 
for  denying  freedom  in  the  sense  revealed  by  intro- 
spection, or  for  supposing  that  mechanical  events  are  not 
determined  by  volitions.  The  problem  of  free  will  versus 
determinism  is  therefore,  if  we  were  right,  mainly  illusory, 
but  in  part  not  yet  capable  of  being  decisively  solved. 


X 

KNOWLEDGE    BY  ACQUAINTANCE 

AND   KNOWLEDGE   BY 

DESCRIPTION 


~^HE  object  of  the  following  paper  is  to  consider  what 
•*•  it  is  that  we  know  in  cases  where  we  know  pro- 
positions about  "the  so-and-so  "  without  knowing  who 
or  what  the  so-and-so  is.  For  example,  I  know  that  the 
candidate  who  gets  most  votes  will  be  elected,  though  I 
do  not  know  who  is  the  candidate  who  will  get  most 
votes.  The  problem  I  wish  to  consider  is  :  What  do  we 
know  in  these  cases,  where  the  subject  is  merely  described? 
I  have  considered  this  problem  elsewhere1  from  a  purely 
logical  point  of  view  ;  but  in  what  follows  I  wish  to  con- 
sider the  question  in  relation  to  theory  of  knowledge  as 
well  as  in  relation  to  logic,  and  in  view  of  the  above- 
mentioned  logical  discussions,  I  shall  in  this  paper  make 
the  logical  portion  as  brief  as  possible. 

In  order  to  make  clear  the  antithesis  between  "ac- 
quaintance "  and  "  description,"  I  shall  first  of  all  try  to 
explain  what  I  mean  by  "acquaintance."  I  say  that  I 
am  acquainted  with  an  object  when  I  have  a  direct 
cognitive  relation  to  that  object,  i.e.  when  I  am  directly 
aware  of  the  object  itself.  When  I  speak  of  a  cognitive 
relation  here,  I  do  not  mean  the  sort  of  relation  which 
constitutes  judgment,  but  the  sort  which  constitutes 
presentation.  In  fact,  I  think  the  relation  of  subject  and 

1  See  references  later. 
P  209 


210  MYSTICISM   AND   LOGIC 

object  which  I  call  acquaintance  is  simply  the  converse 
of  the  relation  of  object  and  subject  which  constitutes 
presentation.  That  is,  to  say  that  S  has  acquaintance 
with  O  is  essentially  the  same  thing  as  to  say  that  O  is 
presented  to  S.  But  the  associations  and  natural  exten- 
sions of  the  word  acquaintance  are  different  from  those  of 
the  word  presentation.  To  begin  with,  as  in  most  cog- 
nitive words,  it  is  natural  to  say  that  I  am  acquainted 
with  an  object  even  at  moments  when  it  is  not  actually 
before  my  mind,  provided  it  has  been  before  my  mind, 
and  will  be  again  whenever  occasion  arises.  This  is  the 
same  sense  in  which  I  am  said  to  know  that  2+2=4  even 
when  I  am  thinking  of  something  else.  In  the  second 
place,  the  word  acquaintance  is  designed  to  emphasise, 
more  than  the  word  presentation,  the  relational  character 
of  the  fact  with  which  we  are  concerned.  There  is,  to  my 
mind,  a  danger  that,  in  speaking  of  presentation,  we 
may  so  emphasis  the  object  as  to  lose  sight  of  the  sub- 
ject. The  result  of  this  is  either  to  lead  to  the  view 
that  there  is  no  subject,  whence  we  arrive  at  materialism  ; 
or  to  lead  to  the  view  that  what  is  presented  is  part  of 
the  subject,  whence  we  arrive  at  idealism,  and  should 
arrive  at  solipsism  but  for  the  most  desperate  contortions. 
Now  I  wish  to  preserve  the  dualism  of  subject  and  object 
in  my  terminology,  because  this  dualism  seems  to  me  a 
fundamental  fact  concerning  cognition.  Hence  I  prefer 
the  word  acquaintance,  because  it  emphasises  the  need  of 
a  subject  which  is  acquainted. 

When  we  ask  what  are  the  kinds  of  objects  with  which 
we  are  acquainted,  the  first  and  most  obvious  example  is 
sense-data.  When  I  see  a  colour  or  hear  a  noise,  I  have 
direct  acquaintance  with  the  colour  or  the  noise.  The 
sense-datum  with  which  I  am  acquainted  in  these  cases 
is  generally,  if  not  always,  complex.  This  is  particularly 


KNOWLEDGE   BY   ACQUAINTANCE      211 

obvious  in  the  case  of  sight.  I  do  not  mean,  of  course, 
merely  that  the  supposed  physical  object  is  complex,  but 
that  the  direct  sensible  object  is  complex  and  contains 
parts  with  spatial  relations.  Whether  it  is  possible  to  be 
aware  of  a  complex  without  being  aware  of  its  con- 
stituents is  not  an  easy  question,  but  on  the  whole  it 
would  seem  that  there  is  no  reason  why  it  should  not 
be  possible.  .  This  question  arises  in  an  acute  form  in 
connection  with  self-consciousness,  which  we  must  now 
briefly  consider. 

In  introspection,  we  seem  to  be  immediately  aware  of 
varying  complexes,  consisting  of  objects  in  various  cog- 
nitive and  conative  relations  to  ourselves.  When  I  see 
the  sun,  it  often  happens  that  I  am  aware  of  my  seeing 
the  sun,  in  addition  to  being  aware  of  the  sun  ;  and  when 
I  desire  food,  it  often  happens  that  I  am  aware  of  my 
desire  for  food.  But  it  is  hard  to  discover  any  state  of 
mind  in  which  I  am  aware  of  myself  alone,  as  opposed  to 
a  complex  of  which  I  am  a  constituent.  The  question  of 
the  nature  of  self-consciousness  is  too  large,  and  too  slightly 
connected  with  our  subject,  to  be  argued  at  length  here.  It 
is  difficult,  but  probably  not  impossible,  to  account  for 
plain  facts  if  we  assume  that  we  do  not  have  acquaintance 
with  ourselves.  It  is  plain  that  we  are  not  only  acquainted 
with  the  complex  "  Self-acquainted-with-A,"  but  we  also 
know  the  proposition  "  I  am  acquainted  with  A."  Now 
here  the  complex  has  been  analysed,  and  if  "  I  "  does  not 
stand  for  something  which  is  a  direct  object  of  acquaint- 
ance, we  shall  have  to  suppose  that  "  I  "  is  something 
known  by  description.  If  we  wished  to  maintain  the  view 
that  there  is  no  acquaintance  with  Self,  we  might  argue 
as  follows  :  We  are  acquainted  with  acquaintance,  and 
we  know  that  it  is  a  relation.  Also  we  are  acquainted 
with  a  complex  in  which  we  perceive  that  acquaintance 


212  MYSTICISM   AND   LOGIC 

is  the  relating  relation.  Hence  we  know  that  this  complex 
must  have  a  constituent  which  is  that  which  is  acquainted, 
i.e.  must  have  a  subject-term  as  well  as  an  object-term. 
This  subject-term  we  define  as  "  I."  Thus  "I"  means 
"  the  subject-term  in  awarenesses  of  which  /  am  aware." 
But  as  a  definition  this  cannot  be  regarded  as  a  happy 
effort.  It  would  seem  necessary,  therefore,  either  to 
suppose  that  I  am  acquainted  with  myself,  and  that  "I," 
therefore,  requires  no  definition,  being  merely  the  proper 
name  of  a  certain  object,  or  to  find  some  other  analysis 
of  self -consciousness.  Thus  self -consciousness  cannot  be 
regarded  as  throwing  light  on  the  question  whether  we 
can  know  a  complex  without  knowing  its  constituents. 
This  question,  however,  is  not  important  for  our  present 
purposes,  and  I  shall  therefore  not  discuss  it  further. 

The  awarenesses  we  have  considered  so  far  have  all 
been  awarenesses  of  particular  existents,  and  might  all 
in  a  large  sense  be  called  sense-data.  For,  from  the  point 
of  view  of  theory  of  knowledge,  introspective  knowledge 
is  exactly  on  a  level  with  knowledge  derived  from  sight 
or  hearing.  But,  in  addition  to  awareness  of  the  above 
kind  of  objects,  which  may  be  called  awareness 
of  particulars,  we  have  also  (though  not  quite  in 
the  same  sense)  what  may  be  called  awareness  of 
universals.  Awareness  of  universals  is  called  conceiving, 
and  a  universal  of  which  we  are  aware  is  called  a  concept. 
Not  only  are  we  aware  of  particular  yellows,  but  if  we 
have  seen  a  sufficient  number  of  yellows  and  have  suffi- 
cient intelligence,  we  are  aware  of  the  universal  yellow  ; 
this  universal  is  the  subject  in  such  judgments  as  "  yellow 
differs  from  blue  "  or  "  yellow  resembles  blue  less  than 
green  does."  And  the  universal  yellow  is  the  predicate  in 
such  judgments  as  "  this  is  yellow,"  where  "  this  "  is  a 
particular  sense-datum.  And  universal  relations,  too, 


KNOWLEDGE   BY  ACQUAINTANCE      213 

are  objects  of  awarenesses ;  up  and  down,  before  and 
after,  resemblance,  desire,  awareness  itself,  and  so  on, 
would  seem  to  be  all  of  them  objects  of  which  we  can  be 
aware. 

In  regard  to  relations,  it  might  be  urged  that  we  are 
never  aware  of  the  universal  relation  itself,  but  only  of 
complexes  in  which  it  is  a  constituent.  For  example,  it 
may  be  said  that  we  do  not  know  directly  such  a  relation 
as  before,  though  we  understand  such  a  proposition  as 
"  this  is  before  that,"  and  may  be  directly  aware  of  such 
a  complex  as  "  this  being  before  that."  This  view,  how- 
ever, is  difficult  to  reconcile  with  the  fact  that  we  often 
know  propositions  in  which  the  relation  is  the  subject, 
or  in  which  the  relata  are  not  definite  given  objects,  but 
"  anything."  For  example,  we  know  that  if  one  thing  is 
before  another,  and  the  other  before  a  third,  then  the 
first  is  before  the  third  ;  and  here  the  things  concerned 
are  not  definite  things,  but  "  anything."  It  is  hard  to 
see  how  we  could  know  such  a  fact  about  "  before  " 
unless  we  were  acquainted  with  "  before,"  and  not  merely 
with  actual  particular  cases  of  one  given  object  being 
before  another  given  object.  And  more  directly  :  A 
judgment  such  as  "  this  is  before  that,"  where  this  judg- 
ment is  derived  from  awareness  of  a  complex,  constitutes 
an  analysis,  and  we  should  not  understand  the  analysis  if 
we  were  not  acquainted  with  the  meaning  of  the  terms 
employed.  Thus  we  must  suppose  that  we  are  acquainted 
with  the  meaning  of  "before,"  and  not  merely  with 
instances  of  it. 

There  are  thus  at  least  two  sorts  of  objects  of  which  we 
are  aware,  namely,  particulars  and  universals.  Among 
particulars  I  include  all  existents,  and  all  complexes  of 
which  one  or  more  constituents  are  existents,  such  as 
this-before-that,  this-above-that,  the-yellowness-of-this. 


214  MYSTICISM   AND   LOGIC 

Among  universals  I  include  all  objects  of  which  no  par- 
ticular is  a  constituent.  Thus  the  disjunction  "  universal- 
particular  "  includes  all  objects.  We  might  also  call  it  the 
disjunction  "  abstract-concrete."  It  is  not  quite  parallel 
with  the  opposition  "  concept-percept,"  because  things 
remembered  or  imagined  belong  with  particulars,  but  can 
hardly  be  called  percepts.  (On  the  other  hand,  universals 
with  which  we  are  acquainted  may  be  identified  with 
concepts.) 

It  will  be  seen  that  among  the  objects  with  which  we 
are  acquainted  are  not  included  physical  objects  (as 
opposed  to  sense-data),  nor  other  people's  minds.  These 
things  are  known  to  us  by  what  I  call  "  knowledge  by 
description,"  which  we  must  now  consider. 

By  a  "  description  "  I  mean  any  phrase  of  the  form  "  a 
so-and-so  "  or  "the  so-and-so."  A  phrase  of  the  form 
"  a  so-and-so  "  I  shall  call  an  "  ambiguous  "  description  ; 
a  phrase  of  the  form  "  the  so-and-so  "  (in  the  singular)  I 
shall  call  a  "  definite  "  description.  Thus  "  a  man  "  is 
an  ambiguous  description,  and  "  the  man  with  the  iron 
mask "  is  a  definite  description.  There  are  various 
problems  connected  with  ambiguous  descriptions,  but  I 
pass  them  by,  since  they  do  not  directly  concern  the  matter 
I  wish  to  discuss.  What  I  wish  to  discuss  is  the  nature  of 
our  knowledge  concerning  objects  in  cases  where  we  know 
that  there  is  an  object  answering  to  a  definite  description, 
though  we  are  not  acquainted  with  any  such  object.  This 
is  a  matter  which  is  concerned  exclusively  with  definite 
descriptions.  I  shall,  therefore,  in  the  sequel,  speak 
simply  of  "  descriptions  "  when  I  mean  "  definite  descrip- 
tions." Thus  a  description  will  mean  any  phrase  of  the 
form  "  the  so-and-so  "  in  the  singular. 

I  shall  say  that  an  object  is  "  known  by  description  " 
when  we  know  that  it  is  "  the  so-and-so,"  i.e.  when  we 


KNOWLEDGE   BY   ACQUAINTANCE      215 

know  that  there  is  one  object,  and  no  more,  having  a 
certain  property  ;  and  it  will  generally  be  implied  that 
we  do  not  have  knowledge  of  the  same  object  by  ac- 
quaintance. We  know  that  the  man  with  the  iron  mask 
existed,  and  many  propositions  are  known  about  him  ; 
but  we  do  not  know  who  he  was.  We  know  that  the 
candidate  who  gets  most  votes  will  be  elected,  and  in  this 
case  we  are  very  likely  also  acquainted  (in  the  only  sense 
in  which  one  can  be  acquainted  with  some  one  else)  with 
the  man  who  is,  in  fact,  the  candidate  who  will  get  most 
votes,  but  we  do  not  know  which  of  the  candidates  he  is, 
i.e.  we  do  not  know  any  proposition  of  the  form  "  A  is 
the  candidate  who  will  get  most  votes  "  where  A  is  one 
of  the  candidates  by  name.  We  shall  say  that  we  have 
"  merely  descriptive  knowledge  "  of  the  so-and-so  when, 
although  we  know  that  the  so-and-so  exists,  and  although 
we  may  possibly  be  acquainted  with  the  object  which  is, 
in  fact,  the  so-and-so,  yet  we  do  not  know  any  pro- 
position "  a  is  the  so-and-so,"  where  a  is  something  with 
which  we  are  acquainted. 

When  we  say  "  the  so-and-so  exists,"  we  mean  that 
there  is  just  one  object  which  is  the  so-and-so.  The  pro- 
position "  a  is  the  so-and-so  "  means  that  a  has  the 
property  so-and-so,  and  nothing  else  has.  "  Sir  Joseph 
Larmor  is  the  Unionist  candidate  "  means  "  Sir  Joseph 
Larmor  is  a  Unionist  candidate,  and  no  one  else  is." 
"  The  Unionist  candidate  exists  "  means  "  some  one  is  a 
Unionist  candidate,  and  no  one  else  is."  Thus,  when  we 
are  acquainted  with  an  object  which  we  know  to  be  the 
so-and-so,  we  know  that  the  so-and-so  exists,  but  we  may 
know  that  the  so-and-so  exists  when  we  are  not  acquainted 
with  any  object  which  we  know  to  be  the  so-and-so,  and 
even  when  we  are  not  acquainted  with  any  object  which,  in 
fact,  is  the  so-and-so. 


216 

Common  words,  even  proper  names,  are  usually  really 
descriptions.  That  is  to  say,  the  thought  in  the  mind  of 
a  person  using  a  proper  name  correctly  can  generally  only 
be  expressed  explicitly  if  we  replace  the  proper  name  by 
a  description.  Moreover,  the  description  required  to 
express  the  thought  will  vary  for  different  people,  or  for 
the  same  person  at  different  times.  The  only  thing 
constant  (so  long  as  the  name  is  rightly  used)  is  the  object 
to  which  the  name  applies.  But  so  long  as  this  remains 
constant,  the  particular  description  involved  usually 
makes  no  difference  to  the  truth  or  falsehood  of  the  pro- 
position in  which  the  name  appears. 

Let  us  take  some  illustrations.  Suppose  some  state- 
ment made  about  Bismarck.  Assuming  that  there  is 
such  a  thing  as  direct  acquaintance  with  oneself,  Bismarck 
himself  might  have  tteed  his  name  directly  to  designate 
the  particular  person  with  whom  he  was  acquainted.  In 
this  case,  if  he  made  a  judgment  about  himself,  he  him- 
self might  be  a  constituent  of  the  judgment.  Here  the 
proper  name  has  the  direct  use  which  it  always  wishes  to 
have,  as  simply  standing  for  a  certain  object,  and  not 
for  a  description  of  the  object.  But  if  a  person  who  knew 
Bismarck  made  a  judgment  about  him,  the  case  is 
different.  What  this  person  was  acquainted  with  were 
certain  sense-data  which  he  connected  (rightly,  we  will 
suppose)  with  Bismarck's  body.  His  body  as  a  physical 
object,  and  still  more  his  mind,  were  only  known  as  the 
body  and  the  mind  connected  with  these  sense-data. 
That  is,  they  were  known  by  description.  It  is,  of  course, 
very  much  a  matter  of  chance  which  characteristics  of  a 
man's  appearance  will  come  into  a  friend's  mind  when 
he  thinks  of  him  ;  thus  the  description  actually  in  the 
friend's  mind  is  accidental.  The  essential  point  is  that 
he  knows  that  the  various  descriptions  all  apply  to  the 


KNOWLEDGE   BY   ACQUAINTANCE      217 

same  entity,  in  spite  of  not  being  acquainted  with  the 
entity  in  question. 

When  we,  who  did  not  know  Bismarck,  make  a  judg- 
ment about  him,  the  description  in  our  minds  will  probably 
be  some  more  or  less  vague  mass  of  historical  knowledge 
— far  more,  in  most  cases,  than  is  required  to  identify 
him.  But,  for  the  sake  of  illustration,  let  us  assume  that 
we  think  of  him  as  "  the  first  Chancellor  of  the  German 
Empire."  Here  all  the  words  are  abstract  except  "  Ger- 
man." The  word  "  German  "  will  again  have  different 
meanings  for  different  people.  To  some  it  will  recall 
travels  in  Germany,  to  some  the  look  of  Germany  on  the 
map,  and  so  on.  But  if  we  are  to  obtain  a  description 
which  we  know  to  be  applicable,  we  shall  be  compelled, 
at  some  point,  to  bring  in  a  reference  to  a  particular  with 
which  we  are  acquainted.  Such  reference  is  involved  in 
any  mention  of  past,  present,  and  future  (as  opposed  to 
definite  dates),  or  of  here  and  there,  or  of  what  others 
have  told  us.  Thus  it  would  seem  that,  in  some  way  or 
other,  a  description  known  to  be  applicable  to  a  particular 
must  involve  some  reference  to  a  particular  with  which 
we  are  acquainted,  if  our  knowledge  about  the  thing 
described  is  not  to  be  merely  what  follows  logically  from 
the  description.  For  example,  "the  most  long-lived  of 
men  "  is  a  description  which  must  apply  to  some  man, 
but  we  can  make  no  judgments  concerning  this  man 
which  involve  knowledge  about  him  beyond  what  the 
description  gives.  If,  however,  we  say,  "  the  first 
Chancellor  of  the  German  Empire  was  an  astute  diplo- 
matist," we  can  only  be  assured  of  the  truth  of  our 
judgment  in  virtue  of  something  with  which  we  are 
acquainted — usually  a  testimony  heard  or  read.  Con- 
sidered psychologically,  apart  from  the  information  we 
convey  to  others,  apart  from  the  fact  about  the  actual 


2i8  MYSTICISM   AND   LOGIC 

Bismarck,  which  gives  importance  to  our  judgment,  the 
thought  we  really  have  contains  the  one  or  more  par- 
ticulars involved,  and  otherwise  consists  wholly  of  con- 
cepts. All  names  of  places — London,  England,  Europe, 
the  earth,  the  Solar  System — similarly  involve,  when 
used,  descriptions  which  start  from  some  one  or  more 
particulars  with  which  we  are  acquainted.  I  suspect  that 
even  the  Universe,  as  considered  by  metaphysics,  involves 
such  a  connection  with  particulars.  In  logic,  on  the 
contrary,  where  we  are  concerned  not  merely  with  what 
does  exist,  but  with  whatever  might  or  could  exist  or  be, 
no  reference  to  actual  particulars  is  involved. 

It  would  seem  that,  when  we  make  a  statement  about 
something  only  known  by  description,  we  often  intend  to 
make  our  statement,  not  in  the  form  involving  the 
description,  but  about  the  actual  thing  described.  That 
is  to  say,  when  we  say  anything  about  Bismarck,  we 
should  like,  if  we  could,  to  make  the  judgment  which 
Bismarck  alone  can  make,  namely,  the  judgment  of  which 
he  himself  is  a  constituent.  In  this  we  are  necessarily 
defeated,  since  the  actual  Bismarck  is  unknown  to  us. 
But  we  know  that  there  is  an  object  B  called  Bismarck, 
and  that  B  was  an  astute  diplomatist.  We  can  thus 
describe  the  proposition  we  should  like  to  affirm,  namely, 
"  B  was  an  astute  diplomatist,"  where  B  is  the  object 
which  was  Bismarck.  What  enables  us  to  communicate 
in  spite  of  the  varying  descriptions  we  employ  is  that  we 
know  there  is  a  true  proposition  concerning  the  actual 
Bismarck,  and  that,  however  we  may  vary  the  description 
(so  long  as  the  description  is  correct),  the  proposition 
described  is  still  the  same.  This  proposition,  which  is 
described  and  is  known  to  be  true,  is  what  interests  us ; 
but  we  are  not  acquainted  with  the  proposition  itself, 
and  do  not  know  it,  though  we  know  it  is  true. 


KNOWLEDGE   BY   ACQUAINTANCE      219 

It  will  be  seen  that  there  are  various  stages  in  the 
removal  from  acquaintance  with  particulars  :  there  is 
Bismarck  to  people  who  knew  him,  Bismarck  to  those 
who  only  know  of  him  through  history,  the  man  with  the 
iron  mask,  the  longest-lived  of  men.  These  are  progres- 
sively further  removed  from  acquaintance  with  particulars, 
and  there  is  a  similar  hierarchy  in  the  region  of  universals. 
Many  universals,  like  many  particulars,  are  only  known 
to  us  by  description.  But  here,  as  in  the  case  of  particu- 
lars, knowledge  concerning  what  is  known  by  description 
is  ultimately  reducible  to  knowledge  concerning  what  is 
known  by  acquaintance. 

The  fundamental  epistemological  principle  in  the 
analysis  of  propositions  containing  descriptions  is  this  : 
Every  proposition  which  we  can  understand  must  be  com- 
posed wholly  of  constituents  with  which  we  are  acquainted. 
From  what  has  been  said  already,  it  will  be  plain  why  I 
advocate  this  principle,  and  how  I  propose  to  meet  the 
case  of  propositions  which  at  first  sight  contravene  it. 
Let  us  begin  with  the  reasons  for  supposing  the  principle 
true. 

The  chief  reason  for  supposing  the  principle  true  is 
that  it  seems  scarcely  possible  to  believe  that  we  can 
make  a  judgment  or  entertain  a  supposition  without 
knowing  what  it  is  that  we  are  judging  or  supposing 
about.  If  we  make  a  judgment  about  (say)  Julius  Caesar, 
it  is  plain  that  the  actual  person  who  was  Julius  Caesar  is 
not  a  constituent  of  the  judgment.  But  before  going 
further,  it  may  be  well  to  explain  what  I  mean  when  I 
say  that  this  or  that  is  a  constituent  of  a  judgment,  or  of 
a  proposition  which  we  understand.  To  begin  with 
judgments  :  a  judgment,  as  an  occurrence,  I  take  to  be 
a  relation  of  a  mind  to  several  entities,  namely,  the 
entities  which  compose  what  is  judged.  If,  e.g.  I  judge 


220  MYSTICISM   AND   LOGIC 

that  A  loves  B,  the  judgment  as  an  event  consists  in  the 
existence,  at  a  certain  moment,  of  a  specific  four-term 
relation,  called  judging,  between  me  and  A  and  love  and 
B.  That  is  to  say,  at  the  time  when  I  judge,  there  is  a 
certain  complex  whose  terms  are  myself  and  A  and  love 
and  B,  and  whose  relating  relation  is  judging.  My  reasons 
tor  this  view  have  been  set  forth  elsewhere,1  and  I  shall  not 
repeat  them  here.  Assuming  this  view  of  judgment,  the 
constituents  of  the  judgment  are  simply  the  constituents  of 
the  complex  which  is  the  judgment.  Thus,  in  the  above 
case,  the  constituents  are  myself  and  A  and  love  and  B 
and  judging.  But  myself  and  judging  are  constituents 
shared  by  all  my  judgments  ;  thus  the  distinctive  con- 
stituents of  the  particular  judgment  in  question  are  A 
and  love  and  B.  Coming  now  to  what  is  meant  by 
"understanding  a  proposition,"  I  should  say  that  there 
is  another  relation  possible  between  me  and  A  and  love 
and  B,  which  is  called  my  supposing  that  A  loves  B.2 
When  we  can  suppose  that  A  loves  B,  we  "  understand 
the  proposition  "  A  loves  B.  Thus  we  often  understand  a 
proposition  in  cases  where  we  have  not  enough  knowledge 
to  make  a  judgment.  Supposing,  like  judging,  is  a  many- 
term  relation,  of  which  a  mind  is  one  term.  The  other 
terms  of  the  relation  are  called  the  constituents  of  the 
proposition  supposed.  Thus  the  principle  which  I 
enunciated  may  be  re-stated  as  follows  :  Whenever  a 

1  Philosophical  Essays,  "  The  Nature  of  Truth."     I  have  been  per- 
suaded by  Mr.  Wittgenstein  that  this  theory  is  somewhat  unduly 
simple,  but  the  modification  which  I  believe  it  to  require  does  not 
affect  the  above  argument  [1917]. 

2  Cf.  Meinong,   Ueber  Annahmen,  passim.     I  formerly  supposed, 
contrary  to  Meinong's  view,  that  the  relationship  of  supposing  might 
be  merely  that  of  presentation.    In  this  view  I  now  think  I  was  mis- 
taken, and  Meinong  is  right.    But  my  present  view  depends  upon  the 
theory  that  both  in  judgment  and  in  assumption  there  is  no  single 
Objective,  but  the  several  constituents  of  the  judgment  or  assumption 
are  in  a  many-term  relation  to  the  mind. 


KNOWLEDGE   BY   ACQUAINTANCE      221 

relation  of  supposing  or  judging  occurs,  the  terms  to  which 
the  supposing  or  judging  mind  is  related  by  the  relation  of 
supposing  or  judging  must  be  terms  with  which  the  mind  in 
question  is  acquainted.  This  is  merely  to  say  that  we 
cannot  make  a  judgment  or  a  supposition  without  know- 
ing what  it  is  that  we  are  making  our  judgment  or  sup- 
position about.  It  seems  to  me  that  the  truth  of  this 
principle  is  evident  as  soon  as  the  principle  is  understood  ; 
I  shall,  therefore,  in  what  follows,  assume  the  principle, 
and  use  it  as  a  guide  in  analysing  judgments  that  contain 
descriptions. 

Returning  now  to  Julius  Caesar,  I  assume  that  it  will 
be  admitted  that  he  himself  is  not  a  constituent  of  any 
judgment  which  I  can  make.  But  at  this  point  it  is 
necessary  to  examine  the  view  that  judgments  are  com- 
posed of  something  called  "ideas,"  and  that  it  is  the 
"  idea  "  of  Julius  Caesar  that  is  a  constituent  of  my 
judgment.  I  believe  the  plausibility  of  this  view  rests 
upon  a  failure  to  form  a  right  theory  of  descriptions.  We 
may  mean  by  my  "  idea  "  of  Julius  Caesar  the  things  that 
I  know  about  him,  e.g.  that  he  conquered  Gaul,  was 
assassinated  on  the  Ides  of  March,  and  is  a  plague  to 
schoolboys.  Now  I  am  admitting,  and  indeed  contending, 
that  in  order  to  discover  what  is  actually  in  my  mind 
when  I  judge  about  Julius  Caesar,  we  must  substitute  for 
the  proper  name  a  description  made  up  of  some  of  the 
things  I  know  about  him.  (A  description  which  will 
often  serve  to  express  my  thought  is  "  the  man  whose 
name  was  Julius  Ccesar."  For  whatever  else  I  may  have 
forgotten  about  him,  it  is  plain  that  when  I  mention  him 
I  have  not  forgotten  that  that  was  his  name.)  But 
although  I  think  the  theory  that  judgments  consist  of 
ideas  may  have  been  suggested  in  some  such  way,  yet  I 
think  the  theory  itself  is  fundamentally  mistaken.  The 


222  MYSTICISM   AND   LOGIC 

view  seems  to  be  that  there  is  some  mental  existent 
which  may  be  called  the  "  idea  "  of  something  outside 
the  mind  of  the  person  who  has  the  idea,  and  that,  since 
judgment  is  a  mental  event,  its  constituents  must  be 
constituents  of  the  mind  of  the  person  judging.  But  in 
this  view  ideas  become  a  veil  between  us  and  outside 
things — we  never  really,  in  knowledge,  attain  to  the 
things  we  are  supposed  to  be  knowing  about,  but  only  to 
the  ideas  of  those  things.  The  relation  of  mind,  idea,  and 
object,  on  this  view,  is  utterly  obscure,  and,  so  far  as  I 
can  see,  nothing  discoverable  by  inspection  warrants  the 
intrusion  of  the  idea  between  the  mind  and  the  object. 
I  suspect  that  the  view  is  fostered  by  the  dislike  of 
relations,  and  that  it  is  felt  the  mind  could  not  know 
objects  unless  there  were  something  "  in "  the  mind 
which  could  be  called  the  state  of  knowing  the  object. 
Such  a  view,  however,  leads  at  once  to  a  vicious  endless 
regress,  since  the  relation  of  idea  to  object  will  have  to  be 
explained  by  supposing  that  the  idea  itself  has  an  idea  of 
the  object,  and  so  on  ad  infinitum.  I  therefore  see  no 
reason  to  believe  that,  when  we  are  acquainted  with  an 
object,  there  is  in  us  something  which  can  be  called  the 
"idea"  of  the  object.  On  the  contrary,  I  hold  that 
acquaintance  is  wholly  a  relation,  not  demanding  any 
such  constituent  of  the  mind  as  is  supposed  by  advocates 
of  "  ideas."  This  is,  of  course,  a  large  question,  and  one 
which  would  take  us  far  from  our  subject  if  it  were 
adequately  discussed.  I  therefore  content  myself  with 
the  above  indications,  and  with  the  corollary  that,  in 
judging,  the  actual  objects  concerning  which  we  judge, 
rather  than  any  supposed  purely  mental  entities,  are 
constituents  of  the  complex  which  is  the  judgment. 

When,  therefore,  I  say  that  we  must  substitute  for 
"t  Julius  Ceesar  "  some  description  of  Julius  Caesar,  in  order 


KNOWLEDGE   BY   ACQUAINTANCE      223 

to  discover  the  meaning  of  a  judgment  nominally  about 
him,  I  am  not  saying  that  we  must  substitute  an  idea. 
Suppose  our  description  is  "  the  man  whose  name  was 
Julius  Ccesar."  Let  our  judgment  be  "  Julius  Caesar  was 
assassinated."  Then  it  becomes  "the  man  whose  name 
was  Julius  Casar  was  assassinated."  Here  Julius  Ccesar 
is  a  noise  or  shape  with  which  we  are  acquainted,  and  all 
the  other  constituents  of  the  judgment  (neglecting  the 
tense  in  "  was  ")  are  concepts  with  which  we  are  ac- 
quainted. Thus  our  judgment  is  wholly  reduced  to  con- 
stituents with  which  we  are  acquainted,  but  Julius  Caesar 
himself  has  ceased  to  be  a  constituent  of  our  judgment. 
This,  however,  requires  a  proviso,  to  be  further  explained 
shortly,  namely,  that  "  the  man  whose  name  was  Julius 
Casar  "  must  not,  as  a  whole,  be  a  constituent  of  our 
judgment,  that  is  to  say,  this  phrase  must  not,  as  a  whole, 
have  a  meaning  which  enters  into  the  judgment.  Any 
right  analysis  of  the  judgment,  therefore,  must  break  up 
this  phrase,  and  not  treat  it  as  a  subordinate  complex 
which  is  part  of  the  judgment.  The  judgment  "  the  man 
whose  name  was  Julius  Ceesar  was  assassinated  "  may 
be  interpreted  as  meaning  "  one  and  only  one  man  was 
called  Julius  Ceesar,  and  that  one  was  assassinated." 
Here  it  is  plain  that  there  is  no  constituent  corresponding 
to  the  phrase  "  the  man  whose  name  was  Julius  Casar." 
Thus  there  is  no  reason  to  regard  this  phrase  as  expressing 
a  constituent  of  the  judgment,  and  we  have  seen  that  this 
phrase  must  be  broken  up  if  we  are  to  be  acquainted  with 
all  the  constituents  of  the  judgment.  This  conclusion, 
which  we  have  reached  from  considerations  concerned 
with  the  theory  of  knowledge,  is  also  forced  upon  us  by 
logical  considerations,  which  must  now  be  briefly  re- 
viewed. 
It  is  common  to  distinguish  two  aspects,  meaning  and 


224  MYSTICISM   AND   LOGIC 

denotation,  in  such  phrases  as  "  the  author  of  Waverley." 
The  meaning  will  be  a  certain  complex,  consisting  (at 
least)  of  authorship  and  Waverley  with  some  relation  ; 
the  denotation  will  be  Scott.  Similarly  "  featherless 
bipeds  "  will  have  a  complex  meaning,  containing  as 
constituents  the  presence  of  two  feet  and  the  absence  of 
feathers,  while  its  denotation  will  be  the  class  of  men. 
Thus  when  we  say  "  Scott  is  the  author  of  Waverley  "  or 
"  men  are  the  same  as  featherless  bipeds,"  we  are  assert- 
ing an  identity  of  denotation,  and  this  assertion  is  worth 
making  because  of  the  diversity  of  meaning.1  I  believe 
that  the  duality  of  meaning  and  denotation,  though 
capable  of  a  true  interpretation,  is  misleading  if  taken  as 
fundamental.  The  denotation,  I  believe,  is  not  a  con- 
stituent of  the  proposition,  except  in  the  case  of  proper 
names,  i.e.  of  words  which  do  not  assign  a  property  to 
an  object,  but  merely  and  solely  name  it.  And  I  should 
hold  further  that,  in  this  sense,  there  are  only  two  words 
which  are  strictly  proper  names  of  particulars,  namely, 
"  I  "  and  "  this."2 

One  reason  for  not  believing  the  denotation  to  be  a  con- 
stituent of  the  proposition  is  that  we  may  know  the  pro- 
position even  when  we  are  not  acquainted  with  the 
denotation.  The  proposition  "  the  author  of  Waverley 
is  a  novelist  "  was  known  to  people  who  did  not  know 
that  "  the  author  of  Waverley  "  denoted  Scott.  This 
reason  has  been  already  sufficiently  emphasised. 

A  second  reason  is  that  propositions  concerning  "  the 
so-and-so  "  are  possible  even  when  "  the  so-and-so  "  has 
no  denotation.  Take,  e.g.  "  the  golden  mountain  does 
not  exist  "  or  "  the  round  square  is  self -contradictory." 

1  This  view  has  been  recently  advocated  by  Miss  E.  E.  C.  Jones, 
"  A  New  Law  of  Thought  and  its  Implications,"  Mind,  January,  1911. 

-  I  should  now  exclude  "I"  from  proper  names  in  the  strict  sense, 
and  retain  only  "this"  [1917]. 


KNOWLEDGE   BY  ACQUAINTANCE      225 

If  we  are  to  preserve  the  duality  of  meaning  and  denota- 
tion, we  have  to  say,  with  Meinong,  that  there  are  such 
objects  as  the  golden  mountain  and  the  round  square, 
although  these  objects  do  not  have  being.  We  even  have 
to  admit  that  the  existent  round  square  is  existent,  but 
does  not  exist.1  Meinong  does  not  regard  this  as  a  con- 
tradiction, but  I  fail  to  see  that  it  is  not  one.  Indeed,  it 
seems  to  me  evident  that  the  judgment  "  there  is  no  such 
object  as  the  round  square  "  does  not  presuppose  that 
there  is  such  an  object.  If  this  is  admitted,  however,  we 
are  led  to  the  conclusion  that,  by  parity  of  form,  no  judg- 
ment concerning  "  the  so-and-so  "  actually  involves  the 
so-and-so  as  a  constituent. 

Miss  Jones2  contends  that  there  is  no  difficulty  in  admit- 
ting contradictory  predicates  concerning  such  an  object 
as  "  the  present  King  of  France,"  on  the  ground  that  this 
object  is  in  itself  contradictory.  Now  it  might,  of  course, 
be  argued  that  this  object,  unlike  the  round  square,  is 
not  self -contradictory,  but  merely  non-existent.  This, 
however,  would  not  go  to  the  root  of  the  matter.  The 
real  objection  to  such  an  argument  is  that  the  law  of 
contradiction  ought  not  to  be  stated  in  the  traditional 
form  "  A  is  not  both  B  and  not  B,"  but  in  the  form  "  no 
proposition  is  both  true  and  false."  The  traditional  form 
only  applies  to  certain  propositions,  namely,  to  those 
which  attribute  a  predicate  to  a  subject.  When  the  law 
is  stated  of  propositions,  instead  of  being  stated  concern- 
ing subjects  and  predicates,  it  is  at  once  evident  that 
propositions  about  the  present  King  of  France  or  the 
round  square  can  form  no  exception,  but  are  just  as  in- 
capable of  being  both  true  and  false  as  other  propositions. 

Miss    Jones3   argues   that    "  Scott   is   the   author   of 

1  Meinong,  Ueber  Annahmen,  2nd  ed.,  Leipzig,  1910,  p.  141. 

2  Mind,  July,  1910,  p.  380.  *  Mind,  July,  1910,  p.  379. 

Q 


226  MYSTICISM   AND   LOGIC 

Waverley  "  asserts  identity  of  denotation  between  Scott 
and  the  author  of  Waverley.  But  there  is  some  difficulty 
in  choosing  among  alternative  meanings  of  this  con- 
tention. In  the  first  place,  it  should  be  observed  that  the 
author  of  Waverley  is  not  a  mere  name,  like  Scott.  Scott  is 
merely  a  noise  or  shape  conventionally  used  to  designate 
a  certain  person  ;  it  gives  us  no  information  about  that 
person,  and  has  nothing  that  can  be  called  meaning  as 
opposed  to  denotation.  (I  neglect  the  fact,  considered 
above,  that  even  proper  names,  as  a  rule,  really  stand  for 
descriptions.)  But  the  author  of  Waverley  is  not  merely 
conventionally  a  name  for  Scott ;  the  element  of  mere 
convention  belongs  here  to  the  separate  words,  the  and 
author  and  of  and  Waverley.  Given  what  these  words 
stand  for,  the  author  of  Waverley  is  no  longer  arbitrary. 
When  it  is  said  that  Scott  is  the  author  of  Waverley,  we 
are  not  stating  that  these  are  two  names  for  one  man,  as 
we  should  be  if  we  said  "  Scott  is  Sir  Walter."  A  man's 
name  is  what  he  is  called,  but  however  rmich  Scott  had 
been  called  the  author  of  Waverley,  that  would  not  have 
made  him  be  the  author ;  it  was  necessary  for  him 
actually  to  write  Waverley,  which  was  a  fact  having 
nothing  to  do  with  names. 

If,  then,  we  are  asserting  identity  of  denotation,  we 
must  not  mean  by  denotation  the  mere  relation  of  a  name 
to  the  thing  named.  In  fact,  it  would  be  nearer  to  the 
truth  to  say  that  the  meaning  of  "  Scott  "  is  the  denota- 
tion of  "  the  author  of  Waverley."  The  relation  of 
"  Scott  "  to  Scott  is  that  "  Scott  "  means  Scott,  just  as 
the  relation  of  "  author  "  to  the  concept  which  is  so  called 
is  that  "  author "  means  this  concept.  Thus  if  we 
distinguish  meaning  and  denotation  in  "  the  author  of 
Waverley,"  we  shall  have  to  say  that  "  Scott  "  has  mean- 
ing but  not  denotation.  Also  when  we  say  "  Scott  is  the 


KNOWLEDGE   BY  ACQUAINTANCE      227 

author  of  Waverley,"  the  meaning  of  "  the  author  of 
Waverley  "  is  relevant  to  our  assertion.  For  if  the 
denotation  alone  were  relevant,  any  other  phrase  with 
the  same  denotation  would  give  the  same  proposition. 
Thus  "  Scott  is  the  author  of  Marmion  "  would  be  the 
same  proposition  as  "  Scott  is  the  author  of  Waverley." 
But  this  is  plainly  not  the  case,  since  from  the  first  we 
learn  that  Scott  wrote  Marmion  and  from  the  second  we 
learn  that  he  wrote  Waverley,  but  the  first  tells  us 
nothing  about  Waverley  and  the  second  nothing  about 
Marmion.  Hence  the  meaning  of  "  the  author  of  Waver- 
ley," as  opposed  to  the  denotation,  is  certainly  relevant 
to  "  Scott  is  the  author  of  Waverley." 

We  have  thus  agreed  that  "  the  author  of  Waverley  " 
is  not  a  mere  name,  and  that  its  meaning  is  relevant  in 
propositions  in  which  it  occurs.  Thus  if  we  are  to  say,  as 
Miss  Jones  does,  that  "  Scott  is  the  author  of  Waverley  " 
asserts  an  identity  of  denotation,  we  must  regard  the 
denotation  of  "  the  author  of  Waverley  "  as  the  denota- 
tion of  what  is  meant  by  "  the  author  of  Waverley."  Let 
us  call  the  meaning  of  "  the  author  of  Waverley  "  M. 
Thus  M  is  what  "  the  author  of  Waverley  "  means.  Then 
we  are  to  suppose  that  "  Scott  is  the  author  of  Waverley  " 
means  "  Scott  is  the  denotation  of  M."  But  here  we  are 
explaining  our  proposition  by  another  of  the  same  form, 
and  thus  we  have  made  no  progress  towards  a  real 
explanation.  "  The  denotation  of  M,"  like  "  the  author 
of  Waverley,"  has  both  meaning  and  denotation,  on  the 
theory  we  are  examining.  If  we  call  its  meaning  M',  our 
proposition  becomes  "  Scott  is  the  denotation  of  M'." 
But  this  leads  at  once  to  an  endless  regress.  Thus  the 
attempt  to  regard  our  proposition  as  asserting  identity 
of  denotation  breaks  down,  and  it  becomes  imperative 
to  find  some  other  analysis.  When  this  analysis  has  been 


228  MYSTICISM   AND   LOGIC 

completed,  we  shall  be  able  to  reinterpret  the  phrase 
"  identity  of  denotation,"  which  remains  obscure  so  long 
as  it  is  taken  as  fundamental. 

The  first  point  to  observe  is  that,  in  any  proposition 
about  "  the  author  of  Waverley,"  provided  Scott  is  not 
explicitly  mentioned,  the  denotation  itself,  i.e.  Scott, 
does  not  occur,  but  only  the  concept  of  denotation,  which 
will  be  represented  by  a  variable.  Suppose  we  say  "  the 
author  of  Waverley  was  the  author  of  Marmion,"  we  are 
certainly  not  saying  that  both  were  Scott — we  may  have 
forgotten  that  there  was  such  a  person  as  Scott.  We  are 
saying  that  there  is  some  man  who  was  the  author  of 
Waverley  and  the  author  of  Marmion.  That  is  to  say, 
there  is  some  one  who  wrote  Waverley  and  Marmion, 
and  no  one  else  wrote  them.  Thus  the  identity  is  that 
of  a  variable,  i.e.  of  an  indefinite  subject,  "  some  one." 
This  is  why  we  can  understand  propositions  about  "  the 
author  of  Waverley,"  without  knowing  who  he  was. 
When  we  say  "  the  author  of  Waverley  was  a  poet,"  we 
mean  "  one  and  only  one  man  wrote  Waverley,  and  he 
was  a  poet  "  ;  when  we  say  "  the  author  of  Waverley 
was  Scott  "  we  mean  "  one  and  only  one  man  wrote 
Waverley,  and  he  was  Scott."  Here  the  identity  is 
between  a  variable,  i.e.  an  indeterminate  subject  ("  he  "), 
and  Scott ;  "  the  author  of  Waverley  "  has  been  analysed 
away,  and  no  longer  appears  as  a  constituent  of  the 
proposition.1 

The  reason  why  it  is  imperative  to  analyse  away  the 
phrase  "  the  author  of  Waverley  "  may  be  stated  as 
follows.  It  is  plain  that  when  we  say  "  the  author  of 
Waverley  is  the  author  of  Marmion,"  the  is  expresses 

1  The  theory  which  I  am  advocating  is  set  forth  fully,  with  the 
logical  grounds  in  its  favour,  in  Principia  Mathematica,  Vol.  I.  Intro- 
duction, Chap.  Ill ;  also,  less  fully,  in  Mind,  October,  1905. 


KNOWLEDGE   BY   ACQUAINTANCE      229 

identity.  We  have  seen  also  that  the  common  denotation, 
namely  Scott,  is  not  a  constituent  of  this  proposition, 
while  the  meanings  (if  any)  of  "  the  author  of  Waverley  " 
and  "  the  author  of  Marmion  "  are  not  identical.  We 
have  seen  also  that,  in  any  sense  in  which  the  meaning  of 
a  word  is  a  constituent  of  a  proposition  in  whose  verbal 
expression  the  word  occurs,  "  Scott "  means  the 
actual  man  Scott,  in  the  same  sense  (so  far  as  concerns 
our  present  discussion)  in  which  "  author "  means 
a  certain  universal.  Thus,  if  "  the  author  of  Waverley  " 
were  a  subordinate  complex  in  the  above  proposition,  its 
meaning  would  have  to  be  what  was  said  to  be  identical 
with  the  meaning  of  "  the  author  of  Marmion."  This  is 
plainly  not  the  case  ;  and  the  only  escape  is  to  say  that 
"  the  author  of  Waverley  "  does  not,  by  itself,  have  a 
meaning,  though  phrases  of  which  it  is  part  do  have  a 
meaning.  That  is,  in  a  right  analysis  of  the  above  pro- 
position, "  the  author  of  Waverley  "  must  disappear. 
This  is  effected  when  the  above  proposition  is  analysed 
as  meaning  :  "  Some  one  wrote  Waverley  and  no  one 
else  did,  and  that  some  one  also  wrote  Marmion  and  no 
one  else  did."  This  may  be  more  simply  expressed  by 
saying  that  the  prepositional  function  "  x  wrote  Waverley 
and  Marmion,  and  no  one  else  did  "  is  capable  of  truth, 
i.e.  some  value  of  x  makes  it  true,  but  no  other  value 
does.  Thus  the  true  subject  of  our  judgment  is  a 
prepositional  function,  i.e.  a  complex  containing  an 
undetermined  constituent,  and  becoming  a  proposition  as 
soon  as  this  constituent  is  determined. 

We  may  now  define  the  denotation  of  a  phrase.  If  we 
know  that  the  proposition  "  a  is  the  so-and-so  "  is  true, 
i.e.  that  a  is  so-and-so  and  nothing  else  is,  we  call  a  the 
denotation  of  the  phrase  "  the  so-and-so."  A  very  great 
many  of  the  propositions  we  naturally  make  about  "  the 

Q2 


230 

so-and-so  "  will  remain  true  or  remain  false  if  we  sub- 
stitute a  for  "  the  so-and-so,"  where  a  is  the  denotation 
of  "  the  so-and-so."  Such  propositions  will  also  remain 
true  or  remain  false  if  we  substitute  for  "  the  so-and-so  " 
any  other  phrase  having  the  same  denotation.  Hence, 
as  practical  men,  we  become  interested  in  the  denotation 
more  than  in  the  description,  since  the  denotation  decides 
as  to  the  truth  or  falsehood  of  so  many  statements  in 
which  the  description  occurs.  Moreover,  as  we  saw 
earlier  in  considering  the  relations  of  description  and 
acquaintance,  we  often  wish  to  reach  the  denotation,  and 
are  only  hindered  by  lack  of  acquaintance  :  in  such  cases 
the  description  is  merely  the  means  we  employ  to  get  as 
near  as  possible  to  the  denotation.  Hence  it  naturally 
comes  to  be  supposed  that  the  denotation  is  part  of  the 
proposition  in  which  the  description  occurs.  But  we 
have  seen,  both  on  logical  and  on  epistemological  grounds, 
that  this  is  an  error.  The  actual  object  (if  any)  which  is 
the  denotation  is  not  (unless  it  is  explicitly  mentioned)  a 
constituent  of  propositions  in  which  descriptions  occur  ; 
and  this  is  the  reason  why,  in  order  to  understand  such 
propositions,  we  need  acquaintance  with  the  constituents 
of  the  description,  but  do  not  need  acquaintance  with  its 
denotation.  The  first  result  of  analysis,  when  applied  to 
propositions  whose  grammatical  subject  is  "  the  so-and- 
so,"  is  to  substitute  a  variable  as  subject ;  i.e.  we  obtain 
a  proposition  of  the  form  :  "  There  is  something  which 
alone  is  so-and-so,  and  that  something  is  such-and-such." 
The  further  analysis  of  propositions  concerning  "  the  so- 
and-so  "  is  thus  merged  in  the  problem  of  the  nature  of 
the  variable,  i.e.  of  the  meanings  of  some,  any,  and  all. 
This  is  a  difficult  problem,  concerning  which  I  do  not 
intend  to  say  anything  at  present. 

To  sum  up  our  whole  discussion  :    We  began  by  dis- 


KNOWLEDGE   BY  ACQUAINTANCE      231 

tinguishing  two  sorts  of  knowledge  of  objects,  namely, 
knowledge  by  acquaintance  and  knowledge  by  description. 
Of  these  it  is  only  the  former  that  brings  the  object  itself 
before  the  mind.  We  have  acquaintance  with  sense-data, 
with  many  universals,  and  possibly  with  ourselves,  but 
not  with  physical  objects  or  other  minds.  We  have 
descriptive  knowledge  of  an  object  when  we  know  that  it 
is  the  object  having  some  property  or  properties  with 
which  we  are  acquainted  ;  that  is  to  say,  when  we  know 
that  the  property  or  properties  in  question  belong  to  one 
object  and  no  more,  we  are  said  to  have  knowledge  of 
that  one  object  by  description,  whether  or  not  we  are 
acquainted  with  the  object.  Our  knowledge  of  physical 
objects  and  of  other  minds  is  only  knowledge  by  descrip- 
tion, the  descriptions  involved  being  usually  such  as 
involve  sense-data.  All  propositions  intelligible  to  us, 
whether  or  not  they  primarily  concern  things  only  known 
to  us  by  description,  are  composed  wholly  of  constituents 
with  which  we  are  acquainted,  for  a  constituent  with  which 
we  are  not  acquainted  is  unintelligible  to  us.  A  judgment, 
we  found,  is  not  composed  of  mental  constituents  called 
"  ideas,"  but  consists  of  an  occurrence  whose  con- 
stituents are  a  mind1  and  certain  objects,  particulars 
or  universals.  (One  at  least  must  be  a  universal.)  When 
a  judgment  is  rightly  analysed,  the  objects  which  are  con- 
stituents of  it  must  all  be  objects  with  which  the  mind 
which  is  a  constituent  of  it  is  acquainted.  This  con- 
clusion forces  us  to  analyse  descriptive  phrases  occurring 
in  propositions,  and  to  say  that  the  objects  denoted  by 
such  phrases  are  not  constituents  of  judgments  in  which 
such  phrases  occur  (unless  these  objects  are  explicitly 

1  I  use  this  phrase  merely  to  denote  the  something  psychological 
which  enters  into  judgment,  without  intending  to  prejudge  the 
question  as  to  what  this  something  is. 


232 

mentioned).  This  leads  us  to  the  view  (recommended 
also  on  purely  logical  grounds)  that  when  we  say  "  the 
author  of  Marmion  was  the  author  of  Waverley,"  Scott 
himself  is  not  a  constituent  of  our  judgment,  and  that 
the  judgment  cannot  be  explained  by  saying  that  it 
affirms  identity  of  denotation  with  diversity  of  meaning. 
It  also,  plainly,  does  not  assert  identity  of  meaning. 
Such  judgments,  therefore,  can  only  be  analysed  by 
breaking  up  the  descriptive  phrases,  introducing  a  vari- 
able, and  making  propositional  functions  the  ultimate 
subjects.  In  fact,  "  the  so-and-so  is  such-and-such  "  will 
mean  that  "  x  is  so-and-so  and  nothing  else  is,  and  x  is 
such-and-such  "  is  capable  of  truth.  The  analysis  of 
such  judgments  involves  many  fresh  problems,  but  the 
discussion  of  these  problems  is  not  undertaken  in  the 
present  paper. 


INDEX 


Achilles    and    the    tortoise,    80    ff, 

89  ff 

Acquaintance,  the  relation  of,  209  ff 
Alexander,  125 
American  Realists,  the,  134 
Aristotle,  42,  76,  97 

Bacon,  41 

Bergson,  14  ff,  22,  105,  128,  185  ff, 

203 

Berkeley,  97,  132 
Blake,  I 
Bosanquet,  99 
Broad,  89  » 

Calculus,  the,  82 

Cantor,  Georg,  64,  81  ff,  85,  91 

Carlyle,  50,  82 

Cause,   the    conception    of,    135   «, 

iSoff 

Christianity  and  renunciation,  51 
Cbuang  Tzu,  106 
Construction  of  permanent  things  and 

matter,  169  ff 
Constructions,  logical,  155  ff 

Darwin,  15,  23,  43 
Dedekind,  64,  81  ff,  85 
Descartes,  97,  126 
Descriptions,  175,  214  ff 

Education,  37  ff 
Euclid,  62,  92,  94 
Evolutionism,  23  ff,  28 

Fano,  93 
Faraday,  34 
Free  will,  205  ff 
Frege,  78  « 


Galileo,  42 
Gladstone,  177 
Good  and  evil,  26  ff 

Hegel,  8,  10,  18,  85,  97,  105  ff 

Heine,  113 

Heraclitus,  i  ff,  10 

Hertz,  34 

Holt,  177  n 

Hume,  i,  97 

Infinite,  the  mathematical,  84  ff 

James,  William,  100 

Jones,  Miss  E.  E.  C,  224  »,  225 

Judgment,  219  ff 


Kant,  85,  96,  97,  99, 
Knowledge  by  acquaintance,  209  ff  ; 
by  description,  2i4"ff 

La  place,  23 

Leibniz,  76,  79,  82  ff,  97,  126,  144, 

1  60 

Locke,  97 
Logic,  the  laws  of,  68  ff 

Macau  lay  and  Taylor's  theorem,  95 

Malthus,  43 

Mathematics,  58  ff;  and  the  Meta- 

physicians, 74  ff  ;  and  logic,  75  ff  ; 

and  the  infinitesimal.  82  ff 
Matter,  the  nature  of,   125  ff;  defi- 

nition of,  164  ff 
Maxwell,  34 

Meaning  and  denotation,  223  ff 
Meinong,  174,  220  »,  225 
Militarism,  50 
Mill,  185,  193  ff 
Mysticism  and  logic,  I  ft 


233 


234 


MYSTICISM   AND   LOGIC 


Necessity,  the  notion  of,  207  ff 
Nietzsche,  22,  50 
Nunn,  125,  137  n,  153 

Parmenides,  7  ff,  18,  21 
Particulars,  awareness  of,  210  ff 
Peano,  78  ff,  93  ff 
Perspectives,   139  ff;    the  space  of, 

158  ff 

Philosophy  and  logic,  1 1 1 
Physics,  sense-data  and,  145  ff 
Pierce,  76  n 

Plato,  i  ff,  10,  30,  60,  97 
Pragmatism,  22,  105 

Realism  and   the  analytic   method, 

120  ff 

Reason  and  intuition,  12  ff 
Relatives,  the  logic  of,  76 
Robb,  167  n 

Santayana,  20 

Sense-data,  147,  210  ff;  and  physics, 
US  ff 


Sensibilia,  148  ff 

Space,  138  ff;  private,  158  ff;  the 
logical  problem,  114  ff;  the  prob- 
lem in  physics,  115  ff;  the  episte- 
mological  problem,  118  ff 

Systems,  deterministic,  199 ;  prac- 
tically isolated,  198 ;  relatively 
isolated,  197  ;  mechanical,  2Oi 

Time,  10,  21  ff,  141  ff,  167  ff 
Tristram   Shandy,   the   paradox  of, 
goff 

Unity  and  Plurality,  18  ff 
Universals,  awareness  of,  212  ff 

Ward,  1 80 

Weierstrass,  80,  82,  95 
Whitehead,  117,  157,  175 
Wolf,  173 

Zeno  the  Eleatic,  64,  80,  84, 
89  ff 


WILLIAM    BKENUON    AND  SON,    LTD.,    PB1MTKRS 
PLYMOUTH,   ENGLAND 


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